Theorem 2exim

Description: Theorem *11.34 in WhiteheadRussell p. 162. Theorem 19.22 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	2exim	$$⊢\forall x\forall y\left(\phi \to \psi \right)\to \left(\exists x\exists y\phi \to \exists x\exists y\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		exim	$$⊢\forall y\left(\phi \to \psi \right)\to \left(\exists y\phi \to \exists y\psi \right)$$
2	1	aleximi	$$⊢\forall x\forall y\left(\phi \to \psi \right)\to \left(\exists x\exists y\phi \to \exists x\exists y\psi \right)$$