Theorem rexlimdva2

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	rexlimdva2.1	$$⊢\left(\left(\phi \wedge x\in A\right)\wedge \psi \right)\to \chi$$
Assertion	rexlimdva2	$$⊢\phi \to \left(\exists x\in A\psi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		rexlimdva2.1	$$⊢\left(\left(\phi \wedge x\in A\right)\wedge \psi \right)\to \chi$$
2	1	exp31	$$⊢\phi \to \left(x\in A\to \left(\psi \to \chi \right)\right)$$
3	2	rexlimdv	$$⊢\phi \to \left(\exists x\in A\psi \to \chi \right)$$