Theorem nfrd 1543

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 1541	. 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 1483

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1533

This theorem depends on definitions:  df-bi 117  df-nf 1484

This theorem is referenced by:  nfan1  1587  nfim1  1594  alrimdd  1632  spimed  1763  cbv2  1772  nfald  1783  sbied  1811  cbvexd  1951  sbcomxyyz  2000  hbsbd  2010  dvelimALT  2038  dvelimfv  2039  hbeud  2076  abidnf  2941  eusvnfb  4501