Metamath Proof Explorer


Theorem nnne0d

Description: A positive integer is nonzero. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis nnge1d.1 ⊢ φ → A ∈ ℕ
Assertion nnne0d ⊢ φ → A ≠ 0

Proof

Step Hyp Ref Expression
1 nnge1d.1 ⊢ φ → A ∈ ℕ
2 nnne0 ⊢ A ∈ ℕ → A ≠ 0
3 1 2 syl ⊢ φ → A ≠ 0