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Theorem cbvrex 2575
 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 2220 . 2
2 nfcv 2220 . 2
3 cbvral.1 . 2
4 cbvral.2 . 2
5 cbvral.3 . 2
61, 2, 3, 4, 5cbvrexf 2573 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wnf 1390  wrex 2350 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355 This theorem is referenced by:  cbvrmo  2577  cbvrexv  2579  cbvrexsv  2590  cbviun  3717  rexxpf  4505  isarep1  5010  rexrnmpt  5336  elabrex  5423
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