Theorem 19.25

Description: Theorem 19.25 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Assertion	19.25	$$⊢\forall y\exists x\left(\phi \to \psi \right)\to \left(\exists y\forall x\phi \to \exists y\exists x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.35	$$⊢\exists x\left(\phi \to \psi \right)\leftrightarrow \left(\forall x\phi \to \exists x\psi \right)$$
2	1	biimpi	$$⊢\exists x\left(\phi \to \psi \right)\to \left(\forall x\phi \to \exists x\psi \right)$$
3	2	aleximi	$$⊢\forall y\exists x\left(\phi \to \psi \right)\to \left(\exists y\forall x\phi \to \exists y\exists x\psi \right)$$