Theorem rexlimivw

Description: Weaker version of rexlimiv . (Contributed by FL, 19-Sep-2011) (Proof shortened by Wolf Lammen, 23-Dec-2024)

	Ref	Expression
Hypothesis	rexlimivw.1	$$⊢\phi \to \psi$$
Assertion	rexlimivw	$$⊢\exists x\in A\phi \to \psi$$

Proof

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