Theorem 2eximi

Description: Inference adding two existential quantifiers to antecedent and consequent. (Contributed by NM, 3-Feb-2005)

	Ref	Expression
Hypothesis	eximi.1	$$⊢\phi \to \psi$$
Assertion	2eximi	$$⊢\exists x\exists y\phi \to \exists x\exists y\psi$$

Proof

Step	Hyp	Ref	Expression
1		eximi.1	$$⊢\phi \to \psi$$
2	1	eximi	$$⊢\exists y\phi \to \exists y\psi$$
3	2	eximi	$$⊢\exists x\exists y\phi \to \exists x\exists y\psi$$