ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  vtocl2g GIF version

Theorem vtocl2g 2611
Description: Implicit substitution of 2 classes for 2 setvar variables. (Contributed by NM, 25-Apr-1995.)
Hypotheses
Ref Expression
vtocl2g.1 (x = A → (φψ))
vtocl2g.2 (y = B → (ψχ))
vtocl2g.3 φ
Assertion
Ref Expression
vtocl2g ((A 𝑉 B 𝑊) → χ)
Distinct variable groups:   x,A   y,A   y,B   ψ,x   χ,y
Allowed substitution hints:   φ(x,y)   ψ(y)   χ(x)   B(x)   𝑉(x,y)   𝑊(x,y)

Proof of Theorem vtocl2g
StepHypRef Expression
1 nfcv 2175 . 2 xA
2 nfcv 2175 . 2 yA
3 nfcv 2175 . 2 yB
4 nfv 1418 . 2 xψ
5 nfv 1418 . 2 yχ
6 vtocl2g.1 . 2 (x = A → (φψ))
7 vtocl2g.2 . 2 (y = B → (ψχ))
8 vtocl2g.3 . 2 φ
91, 2, 3, 4, 5, 6, 7, 8vtocl2gf 2609 1 ((A 𝑉 B 𝑊) → χ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98   = wceq 1242   wcel 1390
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553
This theorem is referenced by:  uniprg  3586  intprg  3639  opthg  3966  opelopabsb  3988  unexb  4143  vtoclr  4331  elimasng  4636  cnvsng  4749  funopg  4877  f1osng  5110  fsng  5279  fvsng  5302  op1stg  5719  op2ndg  5720  xpsneng  6232  xpcomeng  6238  bdunexb  9375  bj-unexg  9376
  Copyright terms: Public domain W3C validator