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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