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Theorem nfcxfrd 2223
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 2221 . 2  |-  ( F/_ x A  <->  F/_ x B )
41, 3sylibr 132 1  |-  ( ph  -> 
F/_ x A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1287   F/_wnfc 2212
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-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-cleq 2078  df-clel 2081  df-nfc 2214
This theorem is referenced by:  nfcsb1d  2950  nfcsbd  2953  nfifd  3404  nfunid  3645  nfiotadxy  4951  nfriotadxy  5579  nfovd  5637  nfnegd  7625
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