Theorem bj-exlimmpi 10581

Description: Lemma for bj-vtoclgf 10586. (Contributed by BJ, 21-Nov-2019.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
bj-exlimmp.nf	|- F/ x ps
bj-exlimmp.min	|- ( ch -> ph )
bj-exlimmpi.maj	|- ( ch -> ( ph -> ps ) )

Assertion

Ref	Expression
bj-exlimmpi	|- ( E. x ch -> ps )

Proof of Theorem bj-exlimmpi

Step	Hyp	Ref	Expression
1		bj-exlimmp.nf	. 2 |- F/ x ps
2		bj-exlimmp.min	. . 3 |- ( ch -> ph )
3		bj-exlimmpi.maj	. . 3 |- ( ch -> ( ph -> ps ) )
4	2, 3	mpd 13	. 2 |- ( ch -> ps )
5	1, 4	exlimi 1525	1 |- ( E. x ch -> ps )

Syntax hints:   -> wi 4   F/wnf 1389   E.wex 1421

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-gen 1378  ax-ie2 1423  ax-4 1440

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

This theorem is referenced by: (None)