Theorem nfrd 1413

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 1411	. 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 1241   F/wnf 1349

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1400

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by:  nfan1  1456  nfim1  1463  alrimdd  1500  spimed  1628  cbv2  1635  nfald  1643  sbied  1671  cbvexd  1802  sbcomxyyz  1846  hbsbd  1858  dvelimALT  1886  dvelimfv  1887  hbeud  1922  abidnf  2709  eusvnfb  4186