Theorem nfrd 1513

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 1511	. 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 1346   F/wnf 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1503

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by:  nfan1  1557  nfim1  1564  alrimdd  1602  spimed  1733  cbv2  1742  nfald  1753  sbied  1781  cbvexd  1920  sbcomxyyz  1965  hbsbd  1975  dvelimALT  2003  dvelimfv  2004  hbeud  2041  abidnf  2898  eusvnfb  4439