Theorem exinst

Description: Existential Instantiation. Virtual deduction form of exlimexi . (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		exinst.1	$$⊢\psi \to \forall x\psi$$
2		exinst.2	$$⊢\left(\exists x\phi ,\phi \to \psi \right)$$
3	2	dfvd2i	$$⊢\exists x\phi \to \left(\phi \to \psi \right)$$
4	1 3	exlimexi	$$⊢\exists x\phi \to \psi$$