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

Theorem vtoclga 2613
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 20-Aug-1995.)
Hypotheses
Ref Expression
vtoclga.1 (x = A → (φψ))
vtoclga.2 (x Bφ)
Assertion
Ref Expression
vtoclga (A Bψ)
Distinct variable groups:   x,A   x,B   ψ,x
Allowed substitution hint:   φ(x)

Proof of Theorem vtoclga
StepHypRef Expression
1 nfcv 2175 . 2 xA
2 nfv 1418 . 2 xψ
3 vtoclga.1 . 2 (x = A → (φψ))
4 vtoclga.2 . 2 (x Bφ)
51, 2, 3, 4vtoclgaf 2612 1 (A Bψ)
Colors of variables: wff set class
Syntax hints:  wi 4  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-bnd 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:  vtoclri  2622  ssuni  3593  ordtriexmid  4210  onsucsssucexmid  4212  tfis3  4252  fvmpt3  5194  fvmptssdm  5198  fnressn  5292  fressnfv  5293  caovord  5614  caovimo  5636  tfrlem1  5864  freccl  5932  nnacl  5998  nnmcl  5999  nnacom  6002  nnaass  6003  nndi  6004  nnmass  6005  nnmsucr  6006  nnmcom  6007  nnsucsssuc  6010  nntri3or  6011  nnaordi  6017  nnaword  6020  nnmordi  6025  nnaordex  6036  indpi  6326  prarloclem3  6480  uzind4s2  8310  cnref1o  8357  frec2uzrdg  8876  expcl2lemap  8921
  Copyright terms: Public domain W3C validator