Theorem rexlimiva

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 18-Dec-2006)

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

Proof

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