Theorem exlimih

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) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 1-Jan-2018)

	Ref	Expression
Hypotheses	exlimih.1	$$⊢\psi \to \forall x\psi$$
	exlimih.2	$$⊢\phi \to \psi$$
Assertion	exlimih	$$⊢\exists x\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		exlimih.1	$$⊢\psi \to \forall x\psi$$
2		exlimih.2	$$⊢\phi \to \psi$$
3	1	nf5i	$$⊢Ⅎx\psi$$
4	3 2	exlimi	$$⊢\exists x\phi \to \psi$$