Theorem rexlimdvw

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 18-Jun-2014)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimdvw.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	a1d	$$⊢\phi \to \left(x\in A\to \left(\psi \to \chi \right)\right)$$
3	2	rexlimdv	$$⊢\phi \to \left(\exists x\in A\psi \to \chi \right)$$