Theorem bj-exlimmpi

Description: Lemma for bj-vtoclg1f1 (an instance of this lemma is a version of bj-vtoclg1f1 where x and y are identified). (Contributed by BJ, 30-Apr-2019) (Proof modification is discouraged.)

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

Proof

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