HomeHome Intuitionistic Logic Explorer
Theorem List (p. 27 of 95)
< Previous  Next >
Bad symbols? Try the
GIF version.

Mirrors  >  Metamath Home Page  >  ILE Home Page  >  Theorem List Contents  >  Recent Proofs       This page: Page List

Theorem List for Intuitionistic Logic Explorer - 2601-2700   *Has distinct variable group(s)
TypeLabelDescription
Statement
 
Theoremvtoclf 2601* Implicit substitution of a class for a setvar variable. This is a generalization of chvar 1637. (Contributed by NM, 30-Aug-1993.)
xψ    &   A V    &   (x = A → (φψ))    &   φ       ψ
 
Theoremvtocl 2602* Implicit substitution of a class for a setvar variable. (Contributed by NM, 30-Aug-1993.)
A V    &   (x = A → (φψ))    &   φ       ψ
 
Theoremvtocl2 2603* Implicit substitution of classes for setvar variables. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
A V    &   B V    &   ((x = A y = B) → (φψ))    &   φ       ψ
 
Theoremvtocl3 2604* Implicit substitution of classes for setvar variables. (Contributed by NM, 3-Jun-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
A V    &   B V    &   𝐶 V    &   ((x = A y = B z = 𝐶) → (φψ))    &   φ       ψ
 
Theoremvtoclb 2605* Implicit substitution of a class for a setvar variable. (Contributed by NM, 23-Dec-1993.)
A V    &   (x = A → (φχ))    &   (x = A → (ψθ))    &   (φψ)       (χθ)
 
Theoremvtoclgf 2606 Implicit substitution of a class for a setvar variable, with bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) (Proof shortened by Mario Carneiro, 10-Oct-2016.)
xA    &   xψ    &   (x = A → (φψ))    &   φ       (A 𝑉ψ)
 
Theoremvtoclg 2607* Implicit substitution of a class expression for a setvar variable. (Contributed by NM, 17-Apr-1995.)
(x = A → (φψ))    &   φ       (A 𝑉ψ)
 
Theoremvtoclbg 2608* Implicit substitution of a class for a setvar variable. (Contributed by NM, 29-Apr-1994.)
(x = A → (φχ))    &   (x = A → (ψθ))    &   (φψ)       (A 𝑉 → (χθ))
 
Theoremvtocl2gf 2609 Implicit substitution of a class for a setvar variable. (Contributed by NM, 25-Apr-1995.)
xA    &   yA    &   yB    &   xψ    &   yχ    &   (x = A → (φψ))    &   (y = B → (ψχ))    &   φ       ((A 𝑉 B 𝑊) → χ)
 
Theoremvtocl3gf 2610 Implicit substitution of a class for a setvar variable. (Contributed by NM, 10-Aug-2013.) (Revised by Mario Carneiro, 10-Oct-2016.)
xA    &   yA    &   zA    &   yB    &   zB    &   z𝐶    &   xψ    &   yχ    &   zθ    &   (x = A → (φψ))    &   (y = B → (ψχ))    &   (z = 𝐶 → (χθ))    &   φ       ((A 𝑉 B 𝑊 𝐶 𝑋) → θ)
 
Theoremvtocl2g 2611* Implicit substitution of 2 classes for 2 setvar variables. (Contributed by NM, 25-Apr-1995.)
(x = A → (φψ))    &   (y = B → (ψχ))    &   φ       ((A 𝑉 B 𝑊) → χ)
 
Theoremvtoclgaf 2612* Implicit substitution of a class for a setvar variable. (Contributed by NM, 17-Feb-2006.) (Revised by Mario Carneiro, 10-Oct-2016.)
xA    &   xψ    &   (x = A → (φψ))    &   (x Bφ)       (A Bψ)
 
Theoremvtoclga 2613* Implicit substitution of a class for a setvar variable. (Contributed by NM, 20-Aug-1995.)
(x = A → (φψ))    &   (x Bφ)       (A Bψ)
 
Theoremvtocl2gaf 2614* Implicit substitution of 2 classes for 2 setvar variables. (Contributed by NM, 10-Aug-2013.)
xA    &   yA    &   yB    &   xψ    &   yχ    &   (x = A → (φψ))    &   (y = B → (ψχ))    &   ((x 𝐶 y 𝐷) → φ)       ((A 𝐶 B 𝐷) → χ)
 
Theoremvtocl2ga 2615* Implicit substitution of 2 classes for 2 setvar variables. (Contributed by NM, 20-Aug-1995.)
(x = A → (φψ))    &   (y = B → (ψχ))    &   ((x 𝐶 y 𝐷) → φ)       ((A 𝐶 B 𝐷) → χ)
 
Theoremvtocl3gaf 2616* Implicit substitution of 3 classes for 3 setvar variables. (Contributed by NM, 10-Aug-2013.) (Revised by Mario Carneiro, 11-Oct-2016.)
xA    &   yA    &   zA    &   yB    &   zB    &   z𝐶    &   xψ    &   yχ    &   zθ    &   (x = A → (φψ))    &   (y = B → (ψχ))    &   (z = 𝐶 → (χθ))    &   ((x 𝑅 y 𝑆 z 𝑇) → φ)       ((A 𝑅 B 𝑆 𝐶 𝑇) → θ)
 
Theoremvtocl3ga 2617* Implicit substitution of 3 classes for 3 setvar variables. (Contributed by NM, 20-Aug-1995.)
(x = A → (φψ))    &   (y = B → (ψχ))    &   (z = 𝐶 → (χθ))    &   ((x 𝐷 y 𝑅 z 𝑆) → φ)       ((A 𝐷 B 𝑅 𝐶 𝑆) → θ)
 
Theoremvtocleg 2618* Implicit substitution of a class for a setvar variable. (Contributed by NM, 10-Jan-2004.)
(x = Aφ)       (A 𝑉φ)
 
Theoremvtoclegft 2619* Implicit substitution of a class for a setvar variable. (Closed theorem version of vtoclef 2620.) (Contributed by NM, 7-Nov-2005.) (Revised by Mario Carneiro, 11-Oct-2016.)
((A B xφ x(x = Aφ)) → φ)
 
Theoremvtoclef 2620* Implicit substitution of a class for a setvar variable. (Contributed by NM, 18-Aug-1993.)
xφ    &   A V    &   (x = Aφ)       φ
 
Theoremvtocle 2621* Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.)
A V    &   (x = Aφ)       φ
 
Theoremvtoclri 2622* Implicit substitution of a class for a setvar variable. (Contributed by NM, 21-Nov-1994.)
(x = A → (φψ))    &   x B φ       (A Bψ)
 
Theoremspcimgft 2623 A closed version of spcimgf 2627. (Contributed by Mario Carneiro, 4-Jan-2017.)
xψ    &   xA       (x(x = A → (φψ)) → (A B → (xφψ)))
 
Theoremspcgft 2624 A closed version of spcgf 2629. (Contributed by Andrew Salmon, 6-Jun-2011.) (Revised by Mario Carneiro, 4-Jan-2017.)
xψ    &   xA       (x(x = A → (φψ)) → (A B → (xφψ)))
 
Theoremspcimegft 2625 A closed version of spcimegf 2628. (Contributed by Mario Carneiro, 4-Jan-2017.)
xψ    &   xA       (x(x = A → (ψφ)) → (A B → (ψxφ)))
 
Theoremspcegft 2626 A closed version of spcegf 2630. (Contributed by Jim Kingdon, 22-Jun-2018.)
xψ    &   xA       (x(x = A → (φψ)) → (A B → (ψxφ)))
 
Theoremspcimgf 2627 Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by Mario Carneiro, 4-Jan-2017.)
xA    &   xψ    &   (x = A → (φψ))       (A 𝑉 → (xφψ))
 
Theoremspcimegf 2628 Existential specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
xA    &   xψ    &   (x = A → (ψφ))       (A 𝑉 → (ψxφ))
 
Theoremspcgf 2629 Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by NM, 2-Feb-1997.) (Revised by Andrew Salmon, 12-Aug-2011.)
xA    &   xψ    &   (x = A → (φψ))       (A 𝑉 → (xφψ))
 
Theoremspcegf 2630 Existential specialization, using implicit substitution. (Contributed by NM, 2-Feb-1997.)
xA    &   xψ    &   (x = A → (φψ))       (A 𝑉 → (ψxφ))
 
Theoremspcimdv 2631* Restricted specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
(φA B)    &   ((φ x = A) → (ψχ))       (φ → (xψχ))
 
Theoremspcdv 2632* Rule of specialization, using implicit substitution. Analogous to rspcdv 2653. (Contributed by David Moews, 1-May-2017.)
(φA B)    &   ((φ x = A) → (ψχ))       (φ → (xψχ))
 
Theoremspcimedv 2633* Restricted existential specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
(φA B)    &   ((φ x = A) → (χψ))       (φ → (χxψ))
 
Theoremspcgv 2634* Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by NM, 22-Jun-1994.)
(x = A → (φψ))       (A 𝑉 → (xφψ))
 
Theoremspcegv 2635* Existential specialization, using implicit substitution. (Contributed by NM, 14-Aug-1994.)
(x = A → (φψ))       (A 𝑉 → (ψxφ))
 
Theoremspc2egv 2636* Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 3-Aug-1995.)
((x = A y = B) → (φψ))       ((A 𝑉 B 𝑊) → (ψxyφ))
 
Theoremspc2gv 2637* Specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 27-Apr-2004.)
((x = A y = B) → (φψ))       ((A 𝑉 B 𝑊) → (xyφψ))
 
Theoremspc3egv 2638* Existential specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.)
((x = A y = B z = 𝐶) → (φψ))       ((A 𝑉 B 𝑊 𝐶 𝑋) → (ψxyzφ))
 
Theoremspc3gv 2639* Specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.)
((x = A y = B z = 𝐶) → (φψ))       ((A 𝑉 B 𝑊 𝐶 𝑋) → (xyzφψ))
 
Theoremspcv 2640* Rule of specialization, using implicit substitution. (Contributed by NM, 22-Jun-1994.)
A V    &   (x = A → (φψ))       (xφψ)
 
Theoremspcev 2641* Existential specialization, using implicit substitution. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Eric Schmidt, 22-Dec-2006.)
A V    &   (x = A → (φψ))       (ψxφ)
 
Theoremspc2ev 2642* Existential specialization, using implicit substitution. (Contributed by NM, 3-Aug-1995.)
A V    &   B V    &   ((x = A y = B) → (φψ))       (ψxyφ)
 
Theoremrspct 2643* A closed version of rspc 2644. (Contributed by Andrew Salmon, 6-Jun-2011.)
xψ       (x(x = A → (φψ)) → (A B → (x B φψ)))
 
Theoremrspc 2644* Restricted specialization, using implicit substitution. (Contributed by NM, 19-Apr-2005.) (Revised by Mario Carneiro, 11-Oct-2016.)
xψ    &   (x = A → (φψ))       (A B → (x B φψ))
 
Theoremrspce 2645* Restricted existential specialization, using implicit substitution. (Contributed by NM, 26-May-1998.) (Revised by Mario Carneiro, 11-Oct-2016.)
xψ    &   (x = A → (φψ))       ((A B ψ) → x B φ)
 
Theoremrspcv 2646* Restricted specialization, using implicit substitution. (Contributed by NM, 26-May-1998.)
(x = A → (φψ))       (A B → (x B φψ))
 
Theoremrspccv 2647* Restricted specialization, using implicit substitution. (Contributed by NM, 2-Feb-2006.)
(x = A → (φψ))       (x B φ → (A Bψ))
 
Theoremrspcva 2648* Restricted specialization, using implicit substitution. (Contributed by NM, 13-Sep-2005.)
(x = A → (φψ))       ((A B x B φ) → ψ)
 
Theoremrspccva 2649* Restricted specialization, using implicit substitution. (Contributed by NM, 26-Jul-2006.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
(x = A → (φψ))       ((x B φ A B) → ψ)
 
Theoremrspcev 2650* Restricted existential specialization, using implicit substitution. (Contributed by NM, 26-May-1998.)
(x = A → (φψ))       ((A B ψ) → x B φ)
 
Theoremrspcimdv 2651* Restricted specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
(φA B)    &   ((φ x = A) → (ψχ))       (φ → (x B ψχ))
 
Theoremrspcimedv 2652* Restricted existential specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
(φA B)    &   ((φ x = A) → (χψ))       (φ → (χx B ψ))
 
Theoremrspcdv 2653* Restricted specialization, using implicit substitution. (Contributed by NM, 17-Feb-2007.) (Revised by Mario Carneiro, 4-Jan-2017.)
(φA B)    &   ((φ x = A) → (ψχ))       (φ → (x B ψχ))
 
Theoremrspcedv 2654* Restricted existential specialization, using implicit substitution. (Contributed by FL, 17-Apr-2007.) (Revised by Mario Carneiro, 4-Jan-2017.)
(φA B)    &   ((φ x = A) → (ψχ))       (φ → (χx B ψ))
 
Theoremrspc2 2655* 2-variable restricted specialization, using implicit substitution. (Contributed by NM, 9-Nov-2012.)
xχ    &   yψ    &   (x = A → (φχ))    &   (y = B → (χψ))       ((A 𝐶 B 𝐷) → (x 𝐶 y 𝐷 φψ))
 
Theoremrspc2v 2656* 2-variable restricted specialization, using implicit substitution. (Contributed by NM, 13-Sep-1999.)
(x = A → (φχ))    &   (y = B → (χψ))       ((A 𝐶 B 𝐷) → (x 𝐶 y 𝐷 φψ))
 
Theoremrspc2va 2657* 2-variable restricted specialization, using implicit substitution. (Contributed by NM, 18-Jun-2014.)
(x = A → (φχ))    &   (y = B → (χψ))       (((A 𝐶 B 𝐷) x 𝐶 y 𝐷 φ) → ψ)
 
Theoremrspc2ev 2658* 2-variable restricted existential specialization, using implicit substitution. (Contributed by NM, 16-Oct-1999.)
(x = A → (φχ))    &   (y = B → (χψ))       ((A 𝐶 B 𝐷 ψ) → x 𝐶 y 𝐷 φ)
 
Theoremrspc3v 2659* 3-variable restricted specialization, using implicit substitution. (Contributed by NM, 10-May-2005.)
(x = A → (φχ))    &   (y = B → (χθ))    &   (z = 𝐶 → (θψ))       ((A 𝑅 B 𝑆 𝐶 𝑇) → (x 𝑅 y 𝑆 z 𝑇 φψ))
 
Theoremrspc3ev 2660* 3-variable restricted existentional specialization, using implicit substitution. (Contributed by NM, 25-Jul-2012.)
(x = A → (φχ))    &   (y = B → (χθ))    &   (z = 𝐶 → (θψ))       (((A 𝑅 B 𝑆 𝐶 𝑇) ψ) → x 𝑅 y 𝑆 z 𝑇 φ)
 
Theoremeqvinc 2661* A variable introduction law for class equality. (Contributed by NM, 14-Apr-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
A V       (A = Bx(x = A x = B))
 
Theoremeqvincg 2662* A variable introduction law for class equality, deduction version. (Contributed by Thierry Arnoux, 2-Mar-2017.)
(A 𝑉 → (A = Bx(x = A x = B)))
 
Theoremeqvincf 2663 A variable introduction law for class equality, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 14-Sep-2003.)
xA    &   xB    &   A V       (A = Bx(x = A x = B))
 
Theoremalexeq 2664* Two ways to express substitution of A for x in φ. (Contributed by NM, 2-Mar-1995.)
A V       (x(x = Aφ) ↔ x(x = A φ))
 
Theoremceqex 2665* Equality implies equivalence with substitution. (Contributed by NM, 2-Mar-1995.)
(x = A → (φx(x = A φ)))
 
Theoremceqsexg 2666* A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. (Contributed by NM, 11-Oct-2004.)
xψ    &   (x = A → (φψ))       (A 𝑉 → (x(x = A φ) ↔ ψ))
 
Theoremceqsexgv 2667* Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 29-Dec-1996.)
(x = A → (φψ))       (A 𝑉 → (x(x = A φ) ↔ ψ))
 
Theoremceqsrexv 2668* Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by NM, 30-Apr-2004.)
(x = A → (φψ))       (A B → (x B (x = A φ) ↔ ψ))
 
Theoremceqsrexbv 2669* Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by Mario Carneiro, 14-Mar-2014.)
(x = A → (φψ))       (x B (x = A φ) ↔ (A B ψ))
 
Theoremceqsrex2v 2670* Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by NM, 29-Oct-2005.)
(x = A → (φψ))    &   (y = B → (ψχ))       ((A 𝐶 B 𝐷) → (x 𝐶 y 𝐷 ((x = A y = B) φ) ↔ χ))
 
Theoremclel2 2671* An alternate definition of class membership when the class is a set. (Contributed by NM, 18-Aug-1993.)
A V       (A Bx(x = Ax B))
 
Theoremclel3g 2672* An alternate definition of class membership when the class is a set. (Contributed by NM, 13-Aug-2005.)
(B 𝑉 → (A Bx(x = B A x)))
 
Theoremclel3 2673* An alternate definition of class membership when the class is a set. (Contributed by NM, 18-Aug-1993.)
B V       (A Bx(x = B A x))
 
Theoremclel4 2674* An alternate definition of class membership when the class is a set. (Contributed by NM, 18-Aug-1993.)
B V       (A Bx(x = BA x))
 
Theorempm13.183 2675* Compare theorem *13.183 in [WhiteheadRussell] p. 178. Only A is required to be a set. (Contributed by Andrew Salmon, 3-Jun-2011.)
(A 𝑉 → (A = Bz(z = Az = B)))
 
Theoremrr19.3v 2676* Restricted quantifier version of Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 25-Oct-2012.)
(x A y A φx A φ)
 
Theoremrr19.28v 2677* Restricted quantifier version of Theorem 19.28 of [Margaris] p. 90. (Contributed by NM, 29-Oct-2012.)
(x A y A (φ ψ) ↔ x A (φ y A ψ))
 
Theoremelabgt 2678* Membership in a class abstraction, using implicit substitution. (Closed theorem version of elabg 2682.) (Contributed by NM, 7-Nov-2005.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
((A B x(x = A → (φψ))) → (A {xφ} ↔ ψ))
 
Theoremelabgf 2679 Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. This version has bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) (Revised by Mario Carneiro, 12-Oct-2016.)
xA    &   xψ    &   (x = A → (φψ))       (A B → (A {xφ} ↔ ψ))
 
Theoremelabf 2680* Membership in a class abstraction, using implicit substitution. (Contributed by NM, 1-Aug-1994.) (Revised by Mario Carneiro, 12-Oct-2016.)
xψ    &   A V    &   (x = A → (φψ))       (A {xφ} ↔ ψ)
 
Theoremelab 2681* Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. (Contributed by NM, 1-Aug-1994.)
A V    &   (x = A → (φψ))       (A {xφ} ↔ ψ)
 
Theoremelabg 2682* Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. (Contributed by NM, 14-Apr-1995.)
(x = A → (φψ))       (A 𝑉 → (A {xφ} ↔ ψ))
 
Theoremelab2g 2683* Membership in a class abstraction, using implicit substitution. (Contributed by NM, 13-Sep-1995.)
(x = A → (φψ))    &   B = {xφ}       (A 𝑉 → (A Bψ))
 
Theoremelab2 2684* Membership in a class abstraction, using implicit substitution. (Contributed by NM, 13-Sep-1995.)
A V    &   (x = A → (φψ))    &   B = {xφ}       (A Bψ)
 
Theoremelab4g 2685* Membership in a class abstraction, using implicit substitution. (Contributed by NM, 17-Oct-2012.)
(x = A → (φψ))    &   B = {xφ}       (A B ↔ (A V ψ))
 
Theoremelab3gf 2686 Membership in a class abstraction, with a weaker antecedent than elabgf 2679. (Contributed by NM, 6-Sep-2011.)
xA    &   xψ    &   (x = A → (φψ))       ((ψA B) → (A {xφ} ↔ ψ))
 
Theoremelab3g 2687* Membership in a class abstraction, with a weaker antecedent than elabg 2682. (Contributed by NM, 29-Aug-2006.)
(x = A → (φψ))       ((ψA B) → (A {xφ} ↔ ψ))
 
Theoremelab3 2688* Membership in a class abstraction using implicit substitution. (Contributed by NM, 10-Nov-2000.)
(ψA V)    &   (x = A → (φψ))       (A {xφ} ↔ ψ)
 
Theoremelrabi 2689* Implication for the membership in a restricted class abstraction. (Contributed by Alexander van der Vekens, 31-Dec-2017.)
(A {x 𝑉φ} → A 𝑉)
 
Theoremelrabf 2690 Membership in a restricted class abstraction, using implicit substitution. This version has bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.)
xA    &   xB    &   xψ    &   (x = A → (φψ))       (A {x Bφ} ↔ (A B ψ))
 
Theoremelrab3t 2691* Membership in a restricted class abstraction, using implicit substitution. (Closed theorem version of elrab3 2693.) (Contributed by Thierry Arnoux, 31-Aug-2017.)
((x(x = A → (φψ)) A B) → (A {x Bφ} ↔ ψ))
 
Theoremelrab 2692* Membership in a restricted class abstraction, using implicit substitution. (Contributed by NM, 21-May-1999.)
(x = A → (φψ))       (A {x Bφ} ↔ (A B ψ))
 
Theoremelrab3 2693* Membership in a restricted class abstraction, using implicit substitution. (Contributed by NM, 5-Oct-2006.)
(x = A → (φψ))       (A B → (A {x Bφ} ↔ ψ))
 
Theoremelrab2 2694* Membership in a class abstraction, using implicit substitution. (Contributed by NM, 2-Nov-2006.)
(x = A → (φψ))    &   𝐶 = {x Bφ}       (A 𝐶 ↔ (A B ψ))
 
Theoremralab 2695* Universal quantification over a class abstraction. (Contributed by Jeff Madsen, 10-Jun-2010.)
(y = x → (φψ))       (x {yφ}χx(ψχ))
 
Theoremralrab 2696* Universal quantification over a restricted class abstraction. (Contributed by Jeff Madsen, 10-Jun-2010.)
(y = x → (φψ))       (x {y Aφ}χx A (ψχ))
 
Theoremrexab 2697* Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 23-Jan-2014.) (Revised by Mario Carneiro, 3-Sep-2015.)
(y = x → (φψ))       (x {yφ}χx(ψ χ))
 
Theoremrexrab 2698* Existential quantification over a class abstraction. (Contributed by Jeff Madsen, 17-Jun-2011.) (Revised by Mario Carneiro, 3-Sep-2015.)
(y = x → (φψ))       (x {y Aφ}χx A (ψ χ))
 
Theoremralab2 2699* Universal quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
(x = y → (ψχ))       (x {yφ}ψy(φχ))
 
Theoremralrab2 2700* Universal quantification over a restricted class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
(x = y → (ψχ))       (x {y Aφ}ψy A (φχ))
    < Previous  Next >

Page List
Jump to page: Contents  1 1-100 2 101-200 3 201-300 4 301-400 5 401-500 6 501-600 7 601-700 8 701-800 9 801-900 10 901-1000 11 1001-1100 12 1101-1200 13 1201-1300 14 1301-1400 15 1401-1500 16 1501-1600 17 1601-1700 18 1701-1800 19 1801-1900 20 1901-2000 21 2001-2100 22 2101-2200 23 2201-2300 24 2301-2400 25 2401-2500 26 2501-2600 27 2601-2700 28 2701-2800 29 2801-2900 30 2901-3000 31 3001-3100 32 3101-3200 33 3201-3300 34 3301-3400 35 3401-3500 36 3501-3600 37 3601-3700 38 3701-3800 39 3801-3900 40 3901-4000 41 4001-4100 42 4101-4200 43 4201-4300 44 4301-4400 45 4401-4500 46 4501-4600 47 4601-4700 48 4701-4800 49 4801-4900 50 4901-5000 51 5001-5100 52 5101-5200 53 5201-5300 54 5301-5400 55 5401-5500 56 5501-5600 57 5601-5700 58 5701-5800 59 5801-5900 60 5901-6000 61 6001-6100 62 6101-6200 63 6201-6300 64 6301-6400 65 6401-6500 66 6501-6600 67 6601-6700 68 6701-6800 69 6801-6900 70 6901-7000 71 7001-7100 72 7101-7200 73 7201-7300 74 7301-7400 75 7401-7500 76 7501-7600 77 7601-7700 78 7701-7800 79 7801-7900 80 7901-8000 81 8001-8100 82 8101-8200 83 8201-8300 84 8301-8400 85 8401-8500 86 8501-8600 87 8601-8700 88 8701-8800 89 8801-8900 90 8901-9000 91 9001-9100 92 9101-9200 93 9201-9300 94 9301-9400 95 9401-9457
  Copyright terms: Public domain < Previous  Next >