Theorem nfcrd 2503

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfeqd.1	|- (ph -> F/_xA)

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/_xA)
2		nfcr 2482	. 2 |- ( F/_xA -> F/x y e. A)
3	1, 2	syl 15	1 |- (ph -> F/x y e. A)

Syntax hints:   -> wi 4   F/wnf 1544   e. wcel 1710   F/_wnfc 2477

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nfc 2479

This theorem is referenced by:  nfeqd  2504  nfeld  2505  dvelimdc  2510  nfcsbd  3170  nfifd  3686