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Theorem nfcxfrd 2487
 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 2485 . 2 (xAxB)
41, 3sylibr 203 1 (φxA)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  Ⅎwnfc 2476 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-cleq 2346  df-clel 2349  df-nfc 2478 This theorem is referenced by:  nfcsb1d  3166  nfcsbd  3169  nfifd  3685  nfunid  3898  nfiotad  4342  nfovd  5544
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