Theorem exim

Description: Theorem 19.22 of Margaris p. 90. (Contributed by NM, 10-Jan-1993) (Proof shortened by Wolf Lammen, 4-Jul-2014)

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

Proof

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