Theorem nf5d 2018

Description: Deduce that x is not free in ps in a context. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
nf5d.1	|- F/ x ph
nf5d.2	|- ( ph -> ( ps -> A. x ps ) )

Assertion

Ref	Expression
nf5d	|- ( ph -> F/ x ps )

Proof of Theorem nf5d

Step	Hyp	Ref	Expression
1		nf5d.1	. . 3 |- F/ x ph
2		nf5d.2	. . 3 |- ( ph -> ( ps -> A. x ps ) )
3	1, 2	alrimi 1515	. 2 |- ( ph -> A. x ( ps -> A. x ps ) )
4		nf5-1 2017	. 2 |- ( A. x ( ps -> A. x ps ) -> F/ x ps )
5	3, 4	syl 14	1 |- ( ph -> F/ x ps )

Syntax hints:   -> wi 4   A.wal 1346   F/wnf 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by:  nfabdw  2331