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Theorem nfcxfrd 2173
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 (φxB)
Assertion
Ref Expression
nfcxfrd (φxA)

Proof of Theorem nfcxfrd
StepHypRef Expression
1 nfcxfrd.2 . 2 (φxB)
2 nfceqi.1 . . 3 A = B
32nfceqi 2171 . 2 (xAxB)
41, 3sylibr 137 1 (φxA)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  wnfc 2162
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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-cleq 2030  df-clel 2033  df-nfc 2164
This theorem is referenced by:  nfcsb1d  2874  nfcsbd  2877  nfifd  3349  nfunid  3578  nfiotadxy  4813  nfriotadxy  5419  nfovd  5477  nfnegd  6984
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