Theorem bj-exlimmpbir

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

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

Proof

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