Theorem nfrd 1544

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 1542	. 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 1371   F/wnf 1484

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1534

This theorem depends on definitions:  df-bi 117  df-nf 1485

This theorem is referenced by:  nfan1  1588  nfim1  1595  alrimdd  1633  spimed  1764  cbv2  1773  nfald  1784  sbied  1812  cbvexd  1952  sbcomxyyz  2001  hbsbd  2011  dvelimALT  2039  dvelimfv  2040  hbeud  2077  abidnf  2948  eusvnfb  4519