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Metamath Proof Explorer

Theorem alrimd

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

Ref Expression
Hypotheses alrimd.1 ⊢ Ⅎ 𝑥 𝜑
alrimd.2 ⊢ Ⅎ 𝑥 𝜓
alrimd.3 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion alrimd ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜒 ) )

Proof

Step Hyp Ref Expression
1 alrimd.1 ⊢ Ⅎ 𝑥 𝜑
2 alrimd.2 ⊢ Ⅎ 𝑥 𝜓
3 alrimd.3 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4 2 a1i ⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )
5 1 4 3 alrimdd ⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜒 ) )