Theorem ralimi

Description: Inference quantifying both antecedent and consequent, with strong hypothesis. (Contributed by NM, 4-Mar-1997)

	Ref	Expression
Hypothesis	ralimi.1	$$⊢\phi \to \psi$$
Assertion	ralimi	$$⊢\forall x\in A\phi \to \forall x\in A\psi$$

Proof

Step	Hyp	Ref	Expression
1		ralimi.1	$$⊢\phi \to \psi$$
2	1	a1i	$$⊢x\in A\to \left(\phi \to \psi \right)$$
3	2	ralimia	$$⊢\forall x\in A\phi \to \forall x\in A\psi$$