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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 (𝜑𝑥𝐵)
Assertion
Ref Expression
nfcxfrd (𝜑𝑥𝐴)

Proof of Theorem nfcxfrd
StepHypRef Expression
1 nfcxfrd.2 . 2 (𝜑𝑥𝐵)
2 nfceqi.1 . . 3 𝐴 = 𝐵
32nfceqi 2221 . 2 (𝑥𝐴𝑥𝐵)
41, 3sylibr 132 1 (𝜑𝑥𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287  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  3643  nfiotadxy  4949  nfriotadxy  5577  nfovd  5635  nfnegd  7622
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