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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 ⊢ 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 )