Theorem exlimexi

Description: Inference similar to Theorem 19.23 of Margaris p. 90. (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	exlimexi.1	$$⊢\psi \to \forall x\psi$$
	exlimexi.2	$$⊢\exists x\phi \to \left(\phi \to \psi \right)$$
Assertion	exlimexi	$$⊢\exists x\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		exlimexi.1	$$⊢\psi \to \forall x\psi$$
2		exlimexi.2	$$⊢\exists x\phi \to \left(\phi \to \psi \right)$$
3		hbe1	$$⊢\exists x\phi \to \forall x\exists x\phi$$
4	3 1 2	exlimdh	$$⊢\exists x\phi \to \left(\exists x\phi \to \psi \right)$$
5	4	pm2.43i	$$⊢\exists x\phi \to \psi$$