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Theorem cbvralv 2527
Description: Change the bound variable of a restricted universal quantifier using implicit substitution. (Contributed by NM, 28-Jan-1997.)
Hypothesis
Ref Expression
cbvralv.1 (x = y → (φψ))
Assertion
Ref Expression
cbvralv (x A φy A ψ)
Distinct variable groups:   x,A   y,A   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvralv
StepHypRef Expression
1 nfv 1418 . 2 yφ
2 nfv 1418 . 2 xψ
3 cbvralv.1 . 2 (x = y → (φψ))
41, 2, 3cbvral 2523 1 (x A φy A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wral 2300
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-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305
This theorem is referenced by:  cbvral2v  2535  cbvral3v  2537  reu7  2730  reusv3i  4157  cnvpom  4803  f1mpt  5353  grprinvlem  5637  grprinvd  5638  tfrlem1  5864  tfrlemiubacc  5885  tfrlemi1  5887  rdgon  5913  cauappcvgprlemladdrl  6628  nnsub  7713  ublbneg  8304  iseqovex  8879  iseqval  8880
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