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| Mirrors > Home > MPE Home > Th. List > nnne0d | Structured version Visualization version GIF version | ||
| Description: A positive integer is nonzero. (Contributed by Mario Carneiro, 27-May-2016.) |
| Ref | Expression |
|---|---|
| nnge1d.1 | ⊢ (𝜑 → 𝐴 ∈ ℕ) |
| Ref | Expression |
|---|---|
| nnne0d | ⊢ (𝜑 → 𝐴 ≠ 0) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nnge1d.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℕ) | |
| 2 | nnne0 12300 | . 2 ⊢ (𝐴 ∈ ℕ → 𝐴 ≠ 0) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐴 ≠ 0) |
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