Theorem rexlimdv3a

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). Frequently-used variant of rexlimdv . (Contributed by NM, 7-Jun-2015)

	Ref	Expression
Hypothesis	rexlimdv3a.1	$$⊢\left(\phi \wedge x\in A\wedge \psi \right)\to \chi$$
Assertion	rexlimdv3a	$$⊢\phi \to \left(\exists x\in A\psi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		rexlimdv3a.1	$$⊢\left(\phi \wedge x\in A\wedge \psi \right)\to \chi$$
2	1	3exp	$$⊢\phi \to \left(x\in A\to \left(\psi \to \chi \right)\right)$$
3	2	rexlimdv	$$⊢\phi \to \left(\exists x\in A\psi \to \chi \right)$$