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Theorem nfcxfrd 2417
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 2415 . 2  |-  ( F/_ x A  <->  F/_ x B )
41, 3sylibr 203 1  |-  ( ph  -> 
F/_ x A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623   F/_wnfc 2406
This theorem is referenced by:  nfcsb1d  3111  nfcsbd  3114  nfifd  3588  nfunid  3834  nfiotad  5222  nfovd  5880  nfriotad  6313  nfnegd  9047
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-cleq 2276  df-clel 2279  df-nfc 2408
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