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Metamath Proof Explorer

Theorem alrimdd

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

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

Proof

Step Hyp Ref Expression
1 alrimdd.1 ⊢ Ⅎ x φ
2 alrimdd.2 ⊢ φ → Ⅎ x ψ
3 alrimdd.3 ⊢ φ → ψ → χ
4 2 nf5rd ⊢ φ → ψ → ∀ x ψ
5 1 3 alimd ⊢ φ → ∀ x ψ → ∀ x χ
6 4 5 syld ⊢ φ → ψ → ∀ x χ