Theorem nfrd 1454

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 1452	. 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 1283   F/wnf 1390

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-4 1441

This theorem depends on definitions:  df-bi 115  df-nf 1391

This theorem is referenced by:  nfan1  1497  nfim1  1504  alrimdd  1541  spimed  1669  cbv2  1676  nfald  1684  sbied  1712  cbvexd  1844  sbcomxyyz  1888  hbsbd  1900  dvelimALT  1928  dvelimfv  1929  hbeud  1964  abidnf  2761  eusvnfb  4212