Theorem nfim1 1581

Description: A closed form of nfim 1582. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 2-Jan-2018.)

Hypotheses

Ref	Expression
nfim1.1	|- F/ x ph
nfim1.2	|- ( ph -> F/ x ps )

Assertion

Ref	Expression
nfim1	|- F/ x ( ph -> ps )

Proof of Theorem nfim1

Step	Hyp	Ref	Expression
1		nfim1.1	. . . 4 |- F/ x ph
2	1	nfri 1529	. . 3 |- ( ph -> A. x ph )
3		nfim1.2	. . . 4 |- ( ph -> F/ x ps )
4	3	nfrd 1530	. . 3 |- ( ph -> ( ps -> A. x ps ) )
5	2, 4	hbim1 1580	. 2 |- ( ( ph -> ps ) -> A. x ( ph -> ps ) )
6	5	nfi 1472	1 |- F/ x ( ph -> ps )

Syntax hints:   -> wi 4   F/wnf 1470

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-gen 1459  ax-4 1520  ax-ial 1544  ax-i5r 1545

This theorem depends on definitions:  df-bi 117  df-nf 1471

This theorem is referenced by:  nfim  1582  cbv1  1755  cbv1v  1757  hbsbd  1992  nfabdw  2348