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Theorem nfcxfrd 2569
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 2567 . 2  |-  ( F/_ x A  <->  F/_ x B )
41, 3sylibr 204 1  |-  ( ph  -> 
F/_ x A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   F/_wnfc 2558
This theorem is referenced by:  nfcsb1d  3273  nfcsbd  3276  nfifd  3754  nfunid  4014  nfiotad  5413  nfovd  6095  nfriotad  6550  nfnegd  9293
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-cleq 2428  df-clel 2431  df-nfc 2560
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