Theorem ralrimivva

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version with double quantification.) (Contributed by Jeff Madsen, 19-Jun-2011)

	Ref	Expression
Hypothesis	ralrimivva.1	$$⊢\left(\phi \wedge \left(x\in A\wedge y\in B\right)\right)\to \psi$$
Assertion	ralrimivva	$$⊢\phi \to \forall x\in A\forall y\in B\psi$$

Proof

Step	Hyp	Ref	Expression
1		ralrimivva.1	$$⊢\left(\phi \wedge \left(x\in A\wedge y\in B\right)\right)\to \psi$$
2	1	ex	$$⊢\phi \to \left(\left(x\in A\wedge y\in B\right)\to \psi \right)$$
3	2	ralrimivv	$$⊢\phi \to \forall x\in A\forall y\in B\psi$$