Theorem nfrd 1534

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 1532	. 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 1362   F/wnf 1474

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1524

This theorem depends on definitions:  df-bi 117  df-nf 1475

This theorem is referenced by:  nfan1  1578  nfim1  1585  alrimdd  1623  spimed  1754  cbv2  1763  nfald  1774  sbied  1802  cbvexd  1942  sbcomxyyz  1991  hbsbd  2001  dvelimALT  2029  dvelimfv  2030  hbeud  2067  abidnf  2932  eusvnfb  4489