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Metamath Proof Explorer

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

Proof

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