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| Mirrors > Home > MPE Home > Th. List > gt0ne0d | Structured version Visualization version GIF version | ||
| Description: Positive implies nonzero. (Contributed by Mario Carneiro, 27-May-2016.) |
| Ref | Expression |
|---|---|
| gt0ne0d.1 | ⊢ (𝜑 → 0 < 𝐴) |
| Ref | Expression |
|---|---|
| gt0ne0d | ⊢ (𝜑 → 𝐴 ≠ 0) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 0re 11263 | . 2 ⊢ 0 ∈ ℝ | |
| 2 | gt0ne0d.1 | . 2 ⊢ (𝜑 → 0 < 𝐴) | |
| 3 | ltne 11358 | . 2 ⊢ ((0 ∈ ℝ ∧ 0 < 𝐴) → 𝐴 ≠ 0) | |
| 4 | 1, 2, 3 | sylancr 587 | 1 ⊢ (𝜑 → 𝐴 ≠ 0) |
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