Theorem ralrimiv

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Nov-1994) Reduce dependencies on axioms. (Revised by Wolf Lammen, 4-Dec-2019)

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

Proof

Step	Hyp	Ref	Expression
1		ralrimiv.1	$$⊢\phi \to \left(x\in A\to \psi \right)$$
2		ax-5	$$⊢\phi \to \forall x\phi$$
3	2 1	hbralrimi	$$⊢\phi \to \forall x\in A\psi$$