Theorem nfrd 1501

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 1499	. 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 1330   F/wnf 1437

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1488

This theorem depends on definitions:  df-bi 116  df-nf 1438

This theorem is referenced by:  nfan1  1544  nfim1  1551  alrimdd  1589  spimed  1719  cbv2  1726  nfald  1734  sbied  1762  cbvexd  1900  sbcomxyyz  1946  hbsbd  1958  dvelimALT  1986  dvelimfv  1987  hbeud  2022  abidnf  2856  eusvnfb  4383