Theorem rexlimdva

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 20-Jan-2007)

	Ref	Expression
Hypothesis	rexlimdva.1	$$⊢\left(\phi \wedge x\in A\right)\to \left(\psi \to \chi \right)$$
Assertion	rexlimdva	$$⊢\phi \to \left(\exists x\in A\psi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		rexlimdva.1	$$⊢\left(\phi \wedge x\in A\right)\to \left(\psi \to \chi \right)$$
2	1	ex	$$⊢\phi \to \left(x\in A\to \left(\psi \to \chi \right)\right)$$
3	2	rexlimdv	$$⊢\phi \to \left(\exists x\in A\psi \to \chi \right)$$