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Metamath Proof Explorer

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	$⊢ ψ \to \forall x ψ$
	exinst.2	$⊢ (\exists x φ, φ \to ψ)$
Assertion	exinst	$⊢ \exists x φ \to ψ$

Proof

Step	Hyp	Ref	Expression
1		exinst.1	$⊢ ψ \to \forall x ψ$
2		exinst.2	$⊢ (\exists x φ, φ \to ψ)$
3	2	dfvd2i	$⊢ \exists x φ \to (φ \to ψ)$
4	1 3	exlimexi	$⊢ \exists x φ \to ψ$