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Metamath Proof Explorer

Theorem rexlimdvva

Description: Inference from Theorem 19.23 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 18-Jun-2014)

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

Step	Hyp	Ref	Expression
1		rexlimdvva.1	$⊢ (φ \land (x \in A \land y \in B)) \to (ψ \to χ)$
2	1	ex	$⊢ φ \to ((x \in A \land y \in B) \to (ψ \to χ))$
3	2	rexlimdvv	$⊢ φ \to (\exists x \in A \exists y \in B ψ \to χ)$