Theorem exlimi

Description: Inference associated with 19.23 . See exlimiv for a version with a disjoint variable condition requiring fewer axioms. (Contributed by NM, 10-Jan-1993) (Revised by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	exlimi.1	$$⊢Ⅎx\psi$$
	exlimi.2	$$⊢\phi \to \psi$$
Assertion	exlimi	$$⊢\exists x\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		exlimi.1	$$⊢Ⅎx\psi$$
2		exlimi.2	$$⊢\phi \to \psi$$
3	1	19.23	$$⊢\forall x\left(\phi \to \psi \right)\leftrightarrow \left(\exists x\phi \to \psi \right)$$
4	3 2	mpgbi	$$⊢\exists x\phi \to \psi$$