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Theorem nfcxfrd 2969
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 2967 . 2 (𝑥𝐴𝑥𝐵)
41, 3sylibr 226 1 (𝜑𝑥𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1658  wnfc 2957
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-12 2222  ax-ext 2804
This theorem depends on definitions:  df-bi 199  df-an 387  df-tru 1662  df-ex 1881  df-nf 1885  df-cleq 2819  df-clel 2822  df-nfc 2959
This theorem is referenced by:  nfcsb1d  3772  nfcsbd  3775  nfifd  4335  nfunid  4666  nfiotad  6090  nfriotad  6875  nfovd  6935  nfnegd  10597  nfxnegd  40464  nfintd  43316  nfiund  43317
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