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	$$⊢\left(x\in A\wedge y\in B\right)\to \left(\phi \to \psi \right)$$
Assertion	rexlimivv	$$⊢\exists x\in A\exists y\in B\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		rexlimivv.1	$$⊢\left(x\in A\wedge y\in B\right)\to \left(\phi \to \psi \right)$$
2	1	rexlimdva	$$⊢x\in A\to \left(\exists y\in B\phi \to \psi \right)$$
3	2	rexlimiv	$$⊢\exists x\in A\exists y\in B\phi \to \psi$$