Theorem eximi

Description: Inference adding existential quantifier to antecedent and consequent. (Contributed by NM, 10-Jan-1993)

	Ref	Expression
Hypothesis	eximi.1	$$⊢\phi \to \psi$$
Assertion	eximi	$$⊢\exists x\phi \to \exists x\psi$$

Proof

Step	Hyp	Ref	Expression
1		eximi.1	$$⊢\phi \to \psi$$
2		exim	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\exists x\phi \to \exists x\psi \right)$$
3	2 1	mpg	$$⊢\exists x\phi \to \exists x\psi$$