Theorem rexlimdv

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 14-Nov-2002) (Proof shortened by Eric Schmidt, 22-Dec-2006) Reduce dependencies on axioms. (Revised by Wolf Lammen, 14-Jan-2020)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimdv.1	$$⊢\phi \to \left(x\in A\to \left(\psi \to \chi \right)\right)$$
2	1	com3l	$$⊢x\in A\to \left(\psi \to \left(\phi \to \chi \right)\right)$$
3	2	rexlimiv	$$⊢\exists x\in A\psi \to \left(\phi \to \chi \right)$$
4	3	com12	$$⊢\phi \to \left(\exists x\in A\psi \to \chi \right)$$