Theorem alrimi

Description: Inference form of Theorem 19.21 of Margaris p. 90, see 19.21 . (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	alrimi.1	⊢ Ⅎ 𝑥 𝜑
	alrimi.2	⊢ ( 𝜑 → 𝜓 )
Assertion	alrimi	⊢ ( 𝜑 → ∀ 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		alrimi.1	⊢ Ⅎ 𝑥 𝜑
2		alrimi.2	⊢ ( 𝜑 → 𝜓 )
3	1	nf5ri	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
4	3 2	alrimih	⊢ ( 𝜑 → ∀ 𝑥 𝜓 )