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Theorem cbvex4v 1802
 Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 26-Jul-1995.)
Hypotheses
Ref Expression
cbvex4v.1 ((x = v y = u) → (φψ))
cbvex4v.2 ((z = f w = g) → (ψχ))
Assertion
Ref Expression
cbvex4v (xyzwφvufgχ)
Distinct variable groups:   z,w,χ   v,u,φ   x,y,ψ   f,g,ψ   w,f   z,g   w,u,x,y,z,v
Allowed substitution hints:   φ(x,y,z,w,f,g)   ψ(z,w,v,u)   χ(x,y,v,u,f,g)

Proof of Theorem cbvex4v
StepHypRef Expression
1 cbvex4v.1 . . . 4 ((x = v y = u) → (φψ))
212exbidv 1745 . . 3 ((x = v y = u) → (zwφzwψ))
32cbvex2v 1796 . 2 (xyzwφvuzwψ)
4 cbvex4v.2 . . . 4 ((z = f w = g) → (ψχ))
54cbvex2v 1796 . . 3 (zwψfgχ)
652exbii 1494 . 2 (vuzwψvufgχ)
73, 6bitri 173 1 (xyzwφvufgχ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98  ∃wex 1378 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424 This theorem depends on definitions:  df-bi 110  df-nf 1347 This theorem is referenced by:  enq0sym  6415  addnq0mo  6430  mulnq0mo  6431  addsrmo  6671  mulsrmo  6672
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