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Metamath Proof Explorer

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)

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 )