Theorem bj-exlimmpbi

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

	Ref	Expression
Hypotheses	bj-exlimmpbi.nf	$$⊢Ⅎx\psi$$
	bj-exlimmpbi.maj	$$⊢\chi \to \left(\phi \leftrightarrow \psi \right)$$
	bj-exlimmpbi.min	$$⊢\phi$$
Assertion	bj-exlimmpbi	$$⊢\exists x\chi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-exlimmpbi.nf	$$⊢Ⅎx\psi$$
2		bj-exlimmpbi.maj	$$⊢\chi \to \left(\phi \leftrightarrow \psi \right)$$
3		bj-exlimmpbi.min	$$⊢\phi$$
4	3 2	mpbii	$$⊢\chi \to \psi$$
5	1 4	exlimi	$$⊢\exists x\chi \to \psi$$