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Theorem cbvrex 2524
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  F/
cbvral.2  F/
cbvral.3
Assertion
Ref Expression
cbvrex
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvrex
StepHypRef Expression
1 nfcv 2175 . 2  F/_
2 nfcv 2175 . 2  F/_
3 cbvral.1 . 2  F/
4 cbvral.2 . 2  F/
5 cbvral.3 . 2
61, 2, 3, 4, 5cbvrexf 2522 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   F/wnf 1346  wrex 2301
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-rex 2306
This theorem is referenced by:  cbvrmo  2526  cbvrexv  2528  cbvrexsv  2539  cbviun  3685  rexxpf  4426  isarep1  4928  rexrnmpt  5253  elabrex  5340
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