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Theorem vtoclga 2596
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 2160 . 2 xA
2 nfv 1402 . 2 xψ
3 vtoclga.1 . 2 (x = A → (φψ))
4 vtoclga.2 . 2 (x Bφ)
51, 2, 3, 4vtoclgaf 2595 1 (A Bψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1228   wcel 1374
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537
This theorem is referenced by:  vtoclri  2605  ssuni  3576  ordtriexmid  4194  onsucsssucexmid  4196  tfis3  4236  fvmpt3  5176  fvmptssdm  5180  fnressn  5274  fressnfv  5275  caovord  5595  caovimo  5617  tfrlem1  5845  tfrlemi14  5869  nnacl  5974  nnmcl  5975  nnacom  5978  nnaass  5979  nndi  5980  nnmass  5981  nnmsucr  5982  nnmcom  5983  nnsucsssuc  5986  nntri3or  5987  nnaordi  5992  nnaword  5995  nnmordi  6000  nnaordex  6011  prarloclem3  6351
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