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Theorem cbvrex 2508
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 31-Jul-2003.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypotheses
Ref Expression
cbvral.1 yφ
cbvral.2 xψ
cbvral.3 (x = y → (φψ))
Assertion
Ref Expression
cbvrex (x A φy A ψ)
Distinct variable groups:   x,A   y,A
Allowed substitution hints:   φ(x,y)   ψ(x,y)

Proof of Theorem cbvrex
StepHypRef Expression
1 nfcv 2160 . 2 xA
2 nfcv 2160 . 2 yA
3 cbvral.1 . 2 yφ
4 cbvral.2 . 2 xψ
5 cbvral.3 . 2 (x = y → (φψ))
61, 2, 3, 4, 5cbvrexf 2506 1 (x A φy A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wnf 1329  wrex 2285
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-nf 1330  df-sb 1628  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290
This theorem is referenced by:  cbvrmo  2510  cbvrexv  2512  cbvrexsv  2523  cbviun  3668  rexxpf  4410  isarep1  4911  rexrnmpt  5235  elabrex  5322
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