Theorem ralrimivw

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 18-Jun-2014)

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

Proof

Step	Hyp	Ref	Expression
1		ralrimivw.1	$$⊢\phi \to \psi$$
2	1	a1d	$$⊢\phi \to \left(x\in A\to \psi \right)$$
3	2	ralrimiv	$$⊢\phi \to \forall x\in A\psi$$