Theorem nfrimi 1518

Description: Moving an antecedent outside F/. (Contributed by Jim Kingdon, 23-Mar-2018.)

Hypotheses

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

Assertion

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

Proof of Theorem nfrimi

Step	Hyp	Ref	Expression
1		nfrimi.1	. 2 |- F/ x ph
2		nfrimi.2	. . . . 5 |- F/ x ( ph -> ps )
3	2	nfri 1512	. . . 4 |- ( ( ph -> ps ) -> A. x ( ph -> ps ) )
4	1	nfri 1512	. . . 4 |- ( ph -> A. x ph )
5		ax-5 1440	. . . 4 |- ( A. x ( ph -> ps ) -> ( A. x ph -> A. x ps ) )
6	3, 4, 5	syl2im 38	. . 3 |- ( ( ph -> ps ) -> ( ph -> A. x ps ) )
7	6	pm2.86i 98	. 2 |- ( ph -> ( ps -> A. x ps ) )
8	1, 7	nfd 1516	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-4 1503

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

This theorem is referenced by:  hbsbd  1975