Theorem 2eximdv

Description: Deduction form of Theorem 19.22 of Margaris p. 90 with two quantifiers, see exim . (Contributed by NM, 3-Aug-1995)

	Ref	Expression
Hypothesis	2alimdv.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	2eximdv	$$⊢\phi \to \left(\exists x\exists y\psi \to \exists x\exists y\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		2alimdv.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	eximdv	$$⊢\phi \to \left(\exists y\psi \to \exists y\chi \right)$$
3	2	eximdv	$$⊢\phi \to \left(\exists x\exists y\psi \to \exists x\exists y\chi \right)$$