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Metamath Proof Explorer

Theorem rexlimivv

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 17-Feb-2004)

		Ref	Expression
	Hypothesis	rexlimivv.1	$⊢ (x \in A \land y \in B) \to (φ \to ψ)$
	Assertion	rexlimivv	$⊢ \exists x \in A \exists y \in B φ \to ψ$

Step	Hyp	Ref	Expression
1		rexlimivv.1	$⊢ (x \in A \land y \in B) \to (φ \to ψ)$
2	1	rexlimdva	$⊢ x \in A \to (\exists y \in B φ \to ψ)$
3	2	rexlimiv	$⊢ \exists x \in A \exists y \in B φ \to ψ$