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Theorem nfcrd 2622
Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfeqd.1  |-  ( ph  -> 
F/_ x A )
Assertion
Ref Expression
nfcrd  |-  ( ph  ->  F/ x  y  e.  A )
Distinct variable groups:    x, y    y, A
Allowed substitution hints:    ph( x, y)    A( x)

Proof of Theorem nfcrd
StepHypRef Expression
1 nfeqd.1 . 2  |-  ( ph  -> 
F/_ x A )
2 nfcr 2607 . 2  |-  ( F/_ x A  ->  F/ x  y  e.  A )
31, 2syl 16 1  |-  ( ph  ->  F/ x  y  e.  A )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   F/wnf 1590    e. wcel 1758   F/_wnfc 2602
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-ex 1588  df-nfc 2604
This theorem is referenced by:  nfeqd  2623  nfeld  2624  dvelimdc  2639  nfcsbd  3413  nfifd  3926  axextnd  8867  axrepndlem1  8868  axunndlem1  8871  axregnd  8882  axregndOLD  8883  axextdist  27758
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