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Theorem nfcxfrd 2256
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 2254 . 2 (𝑥𝐴𝑥𝐵)
41, 3sylibr 133 1 (𝜑𝑥𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1316  wnfc 2245
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-cleq 2110  df-clel 2113  df-nfc 2247
This theorem is referenced by:  nfcsb1d  3003  nfcsbd  3006  nfifd  3469  nfunid  3713  nfiotadxy  5061  nfriotadxy  5706  nfovd  5768  nfnegd  7926
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