Theorem bj-exlimmpbir 31507

Description: Lemma for theorems of the vtoclg 3106 family. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
bj-exlimmpbir	|- ( E. x ch -> ph )

Proof of Theorem bj-exlimmpbir

Step	Hyp	Ref	Expression
1		bj-exlimmpbir.nf	. 2 |- F/ x ph
2		bj-exlimmpbir.min	. . 3 |- ps
3		bj-exlimmpbir.maj	. . 3 |- ( ch -> ( ph <-> ps ) )
4	2, 3	mpbiri 237	. 2 |- ( ch -> ph )
5	1, 4	exlimi 1994	1 |- ( E. x ch -> ph )

Syntax hints:   -> wi 4   <-> wb 188   E.wex 1662   F/wnf 1666

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-12 1932

This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667

This theorem is referenced by: (None)