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Theorem nfcxfrd 2750
 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 2748 . 2 (𝑥𝐴𝑥𝐵)
41, 3sylibr 223 1 (𝜑𝑥𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475  Ⅎwnfc 2738 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-cleq 2603  df-clel 2606  df-nfc 2740 This theorem is referenced by:  nfcsb1d  3513  nfcsbd  3516  nfifd  4064  nfunid  4379  nfiotad  5771  nfriotad  6519  nfovd  6574  nfnegd  10155  nfintd  42218  nfiund  42219
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