Theorem reximia

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 10-Feb-1997)

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

Proof

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