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Theorem cbvrex 2651
 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
cbvral.2
cbvral.3
Assertion
Ref Expression
cbvrex
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvrex
StepHypRef Expression
1 nfcv 2281 . 2
2 nfcv 2281 . 2
3 cbvral.1 . 2
4 cbvral.2 . 2
5 cbvral.3 . 2
61, 2, 3, 4, 5cbvrexf 2649 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wnf 1436  wrex 2417 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422 This theorem is referenced by:  cbvrmo  2653  cbvrexv  2655  cbvrexsv  2669  cbviun  3850  disjiun  3924  rexxpf  4686  isarep1  5209  rexrnmpt  5563  elabrex  5659
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