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Metamath Proof Explorer

Theorem alrimi

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

Ref Expression
Hypotheses alrimi.1 ⊢ Ⅎ x φ
alrimi.2 ⊢ φ → ψ
Assertion alrimi ⊢ φ → ∀ x ψ

Proof

Step Hyp Ref Expression
1 alrimi.1 ⊢ Ⅎ x φ
2 alrimi.2 ⊢ φ → ψ
3 1 nf5ri ⊢ φ → ∀ x φ
4 3 2 alrimih ⊢ φ → ∀ x ψ