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Theorem nfcxfrd 2218
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 2216 . 2 (𝑥𝐴𝑥𝐵)
41, 3sylibr 132 1 (𝜑𝑥𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1285  wnfc 2207
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-cleq 2075  df-clel 2078  df-nfc 2209
This theorem is referenced by:  nfcsb1d  2937  nfcsbd  2940  nfifd  3384  nfunid  3616  nfiotadxy  4900  nfriotadxy  5507  nfovd  5565  nfnegd  7371
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