Theorem ralimiaa

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 4-Aug-2007)

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

Proof

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