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Theorem nfcxfrd 2158
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 2156 . 2 (xAxB)
41, 3sylibr 137 1 (φxA)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1228  wnfc 2147
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 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-17 1400  ax-ial 1409  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-cleq 2015  df-clel 2018  df-nfc 2149
This theorem is referenced by:  nfcsb1d  2857  nfcsbd  2860  nfifd  3332  nfunid  3561  nfiotadxy  4797  nfriotadxy  5400  nfovd  5458  nfnegd  6800
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