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Theorem nfcrd 2445
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 2424 . 2  |-  ( F/_ x A  ->  F/ x  y  e.  A )
31, 2syl 15 1  |-  ( ph  ->  F/ x  y  e.  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1534    e. wcel 1696   F/_wnfc 2419
This theorem is referenced by:  nfeqd  2446  nfeld  2447  dvelimdc  2452  nfcsbd  3127  nfifd  3601  axrepndlem1  8230
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-nfc 2421
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