Metamath Proof Explorer


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 𝑥 𝜑
alrimi.2 ( 𝜑𝜓 )
Assertion alrimi ( 𝜑 → ∀ 𝑥 𝜓 )

Proof

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