Theorem alrimih

Description: Inference form of Theorem 19.21 of Margaris p. 90. See 19.21 and 19.21h . Instance of sylg . (Contributed by NM, 9-Jan-1993) (Revised by BJ, 31-Mar-2021)

	Ref	Expression
Hypotheses	alrimih.1	$$⊢\phi \to \forall x\phi$$
	alrimih.2	$$⊢\phi \to \psi$$
Assertion	alrimih	$$⊢\phi \to \forall x\psi$$

Proof

Step	Hyp	Ref	Expression
1		alrimih.1	$$⊢\phi \to \forall x\phi$$
2		alrimih.2	$$⊢\phi \to \psi$$
3	1 2	sylg	$$⊢\phi \to \forall x\psi$$