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Theorem nfcxfrd 2902
Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfcxfr.1 𝐴 = 𝐵
nfcxfrd.2 (𝜑𝑥𝐵)
Assertion
Ref Expression
nfcxfrd (𝜑𝑥𝐴)

Proof of Theorem nfcxfrd
StepHypRef Expression
1 nfcxfrd.2 . 2 (𝜑𝑥𝐵)
2 nfcxfr.1 . . 3 𝐴 = 𝐵
32nfceqi 2900 . 2 (𝑥𝐴𝑥𝐵)
41, 3sylibr 234 1 (𝜑𝑥𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537  wnfc 2888
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-nf 1781  df-cleq 2727  df-clel 2814  df-nfc 2890
This theorem is referenced by:  nfcsb1d  3931  nfcsbd  3934  nfcsbw  3935  nfifd  4560  nfunid  4918  nfopabd  5216  nfiotadw  6519  nfiotad  6521  nfriotadw  7396  nfriotad  7399  nfovd  7460  nfttrcld  9748  nfnegd  11501  nfxnegd  45391  nfintd  48904  nfiund  48905  nfiundg  48906
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