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Metamath Proof Explorer

Theorem alrimiv

Description: Inference form of Theorem 19.21 of Margaris p. 90. See 19.21 and 19.21v . (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypothesis alrimiv.1 ⊢ ( 𝜑 → 𝜓 )
Assertion alrimiv ( 𝜑 → ∀ 𝑥 𝜓 )

Proof

Step Hyp Ref Expression
1 alrimiv.1 ⊢ ( 𝜑 → 𝜓 )
2 ax-5 ⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3 2 1 alrimih ⊢ ( 𝜑 → ∀ 𝑥 𝜓 )