Theorem nfim1 2022

Description: A closed form of nfim 2023. (Contributed by NM, 2-Jun-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 1972	. . 3 |- ( ph -> A. x ph )
3		nfim1.2	. . . 4 |- ( ph -> F/ x ps )
4	3	nfrd 1973	. . 3 |- ( ph -> ( ps -> A. x ps ) )
5	2, 4	hbim1 2021	. 2 |- ( ( ph -> ps ) -> A. x ( ph -> ps ) )
6	5	nfi 1682	1 |- F/ x ( ph -> ps )

Syntax hints:   -> wi 4   F/wnf 1675

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950

This theorem depends on definitions:  df-bi 190  df-ex 1672  df-nf 1676

This theorem is referenced by:  nfim  2023  cbv1  2123  dvelimdf  2184  sbied  2258  sbco2d  2265  bj-cbv1v  31396