Theorem nfrd 1566

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 1564	. 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 1393   F/wnf 1506

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1556

This theorem depends on definitions:  df-bi 117  df-nf 1507

This theorem is referenced by:  nfan1  1610  nfim1  1617  alrimdd  1655  spimed  1786  cbv2  1795  nfald  1806  sbied  1834  cbvexd  1974  sbcomxyyz  2023  hbsbd  2033  dvelimALT  2061  dvelimfv  2062  hbeud  2099  abidnf  2971  eusvnfb  4545