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Metamath Proof Explorer

Theorem rexlimdvv

Description: Inference from Theorem 19.23 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Jul-2004)

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

Step	Hyp	Ref	Expression
1		rexlimdvv.1	$⊢ φ \to ((x \in A \land y \in B) \to (ψ \to χ))$
2	1	expdimp	$⊢ (φ \land x \in A) \to (y \in B \to (ψ \to χ))$
3	2	rexlimdv	$⊢ (φ \land x \in A) \to (\exists y \in B ψ \to χ)$
4	3	rexlimdva	$⊢ φ \to (\exists x \in A \exists y \in B ψ \to χ)$