Theorem ralrimiva

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 2-Jan-2006)

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

Proof

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