Theorem rexlimdvaa

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by Mario Carneiro, 15-Jun-2016)

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

Proof

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