Theorem nfcrd 2771

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

Step	Hyp	Ref	Expression
1		nfeqd.1	. 2 |- ( ph -> F/_ x A )
2		nfcr 2756	. 2 |- ( F/_ x A -> F/ x y e. A )
3	1, 2	syl 17	1 |- ( ph -> F/ x y e. A )

Syntax hints:   -> wi 4   F/wnf 1708   e. wcel 1990   F/_wnfc 2751

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nfc 2753

This theorem is referenced by:  nfeqd  2772  nfeld  2773  dvelimdc  2786  nfcsbd  3550  nfifd  4114  axextnd  9413  axrepndlem1  9414  axunndlem1  9417  axregnd  9426  axextdist  31705  nfintd  42420  nfiund  42421