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| Mirrors > Home > MPE Home > Th. List > rpne0d | Structured version Visualization version GIF version | ||
| Description: A positive real is nonzero. (Contributed by Mario Carneiro, 28-May-2016.) |
| Ref | Expression |
|---|---|
| rpred.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ+) |
| Ref | Expression |
|---|---|
| rpne0d | ⊢ (𝜑 → 𝐴 ≠ 0) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rpred.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ+) | |
| 2 | rpne0 13051 | . 2 ⊢ (𝐴 ∈ ℝ+ → 𝐴 ≠ 0) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐴 ≠ 0) |
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