Theorem nfrimi 1458

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 1452	. . . 4 |- ( ( ph -> ps ) -> A. x ( ph -> ps ) )
4	1	nfri 1452	. . . 4 |- ( ph -> A. x ph )
5		ax-5 1376	. . . 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 97	. 2 |- ( ph -> ( ps -> A. x ps ) )
8	1, 7	nfd 1456	1 |- ( ph -> F/ x ps )

Syntax hints:   -> wi 4   A.wal 1282   F/wnf 1389

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-4 1440

This theorem depends on definitions:  df-bi 115  df-nf 1390

This theorem is referenced by:  hbsbd  1899