Theorem nfrd 1569

Description: Consequence of the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfrd.1	|- ( ph -> F/ x ps )

Assertion

Ref	Expression
nfrd	|- ( ph -> ( ps -> A. x ps ) )

Proof of Theorem nfrd

Step	Hyp	Ref	Expression
1		nfrd.1	. 2 |- ( ph -> F/ x ps )
2		nfr 1567	. 2 |- ( F/ x ps -> ( ps -> A. x ps ) )
3	1, 2	syl 14	1 |- ( ph -> ( ps -> A. x ps ) )

Syntax hints:   -> wi 4   A.wal 1396   F/wnf 1509

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1559

This theorem depends on definitions:  df-bi 117  df-nf 1510

This theorem is referenced by:  nfan1  1613  nfim1  1620  alrimdd  1658  spimed  1789  cbv2  1798  nfald  1809  sbied  1837  cbvexd  1979  sbcomxyyz  2028  hbsbd  2038  dvelimALT  2066  dvelimfv  2067  hbeud  2104  abidnf  2988  eusvnfb  4580