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	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
	alrimih.2	⊢ ( 𝜑 → 𝜓 )
Assertion	alrimih	⊢ ( 𝜑 → ∀ 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		alrimih.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
2		alrimih.2	⊢ ( 𝜑 → 𝜓 )
3	1 2	sylg	⊢ ( 𝜑 → ∀ 𝑥 𝜓 )