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Theorem nfcxfrd 2254
Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfceqi.1  |-  A  =  B
nfcxfrd.2  |-  ( ph  -> 
F/_ x B )
Assertion
Ref Expression
nfcxfrd  |-  ( ph  -> 
F/_ x A )

Proof of Theorem nfcxfrd
StepHypRef Expression
1 nfcxfrd.2 . 2  |-  ( ph  -> 
F/_ x B )
2 nfceqi.1 . . 3  |-  A  =  B
32nfceqi 2252 . 2  |-  ( F/_ x A  <->  F/_ x B )
41, 3sylibr 133 1  |-  ( ph  -> 
F/_ x A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1314   F/_wnfc 2243
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-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-17 1489  ax-ial 1497  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-cleq 2108  df-clel 2111  df-nfc 2245
This theorem is referenced by:  nfcsb1d  3001  nfcsbd  3004  nfifd  3467  nfunid  3711  nfiotadxy  5059  nfriotadxy  5704  nfovd  5766  nfnegd  7922
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