Theorem alimi

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 5-Jan-1993)

	Ref	Expression
Hypothesis	alimi.1	$$⊢\phi \to \psi$$
Assertion	alimi	$$⊢\forall x\phi \to \forall x\psi$$

Proof

Step	Hyp	Ref	Expression
1		alimi.1	$$⊢\phi \to \psi$$
2		alim	$$⊢\forall x\left(\phi \to \psi \right)\to \left(\forall x\phi \to \forall x\psi \right)$$
3	2 1	mpg	$$⊢\forall x\phi \to \forall x\psi$$