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Theorem nfcxfrd 2176
 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 2174 . 2 (𝑥𝐴𝑥𝐵)
41, 3sylibr 137 1 (𝜑𝑥𝐴)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1243  Ⅎwnfc 2165 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-cleq 2033  df-clel 2036  df-nfc 2167 This theorem is referenced by:  nfcsb1d  2880  nfcsbd  2883  nfifd  3355  nfunid  3587  nfiotadxy  4870  nfriotadxy  5476  nfovd  5534  nfnegd  7207
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