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	$$⊢Ⅎx\phi$$
	bj-exlimmpbir.maj	$$⊢\chi \to \left(\phi \leftrightarrow \psi \right)$$
	bj-exlimmpbir.min	$$⊢\psi$$
Assertion	bj-exlimmpbir	$$⊢\exists x\chi \to \phi$$

Proof

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