Theorem ralimia

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 19-Jul-1996)

	Ref	Expression
Hypothesis	ralimia.1	$$⊢x\in A\to \left(\phi \to \psi \right)$$
Assertion	ralimia	$$⊢\forall x\in A\phi \to \forall x\in A\psi$$

Proof

Step	Hyp	Ref	Expression
1		ralimia.1	$$⊢x\in A\to \left(\phi \to \psi \right)$$
2	1	a2i	$$⊢\left(x\in A\to \phi \right)\to \left(x\in A\to \psi \right)$$
3	2	ralimi2	$$⊢\forall x\in A\phi \to \forall x\in A\psi$$