Theorem ralrimi

Description: Inference from Theorem 19.21 of Margaris p. 90 (restricted quantifier version). For a version based on fewer axioms see ralrimiv . (Contributed by NM, 10-Oct-1999) Shortened after introduction of hbralrimi . (Revised by Wolf Lammen, 4-Dec-2019)

	Ref	Expression
Hypotheses	ralrimi.1	$$⊢Ⅎx\phi$$
	ralrimi.2	$$⊢\phi \to \left(x\in A\to \psi \right)$$
Assertion	ralrimi	$$⊢\phi \to \forall x\in A\psi$$

Proof

Step	Hyp	Ref	Expression
1		ralrimi.1	$$⊢Ⅎx\phi$$
2		ralrimi.2	$$⊢\phi \to \left(x\in A\to \psi \right)$$
3	1	nf5ri	$$⊢\phi \to \forall x\phi$$
4	3 2	hbralrimi	$$⊢\phi \to \forall x\in A\psi$$