Theorem reximi

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 18-Oct-1996)

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

Proof

Step	Hyp	Ref	Expression
1		ralimi.1	$$⊢\phi \to \psi$$
2	1	a1i	$$⊢x\in A\to \left(\phi \to \psi \right)$$
3	2	reximia	$$⊢\exists x\in A\phi \to \exists x\in A\psi$$