Theorem nfcrd 2191

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 2170	. 2 |- ( F/_ x A -> F/ x y e. A )
3	1, 2	syl 14	1 |- ( ph -> F/ x y e. A )

Syntax hints:   -> wi 4   F/wnf 1349   e. wcel 1393   F/_wnfc 2165

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1400

This theorem depends on definitions:  df-bi 110  df-nfc 2167

This theorem is referenced by:  nfeqd  2192  nfeld  2193  dvelimdc  2197  nfcsbd  2883  nfifd  3355