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Theorem nfcrd 2313
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 2291 . 2  |-  ( F/_ x A  ->  F/ x  y  e.  A )
31, 2syl 14 1  |-  ( ph  ->  F/ x  y  e.  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1440    e. wcel 2128   F/_wnfc 2286
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1490
This theorem depends on definitions:  df-bi 116  df-nfc 2288
This theorem is referenced by:  nfeqd  2314  nfeld  2315  dvelimdc  2320  nfcsbd  3066  nfcsbw  3067  nfifd  3532
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