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| Mirrors > Home > MPE Home > Th. List > nn0ge0d | Structured version Visualization version GIF version | ||
| Description: A nonnegative integer is greater than or equal to zero. (Contributed by Mario Carneiro, 27-May-2016.) |
| Ref | Expression |
|---|---|
| nn0red.1 | ⊢ (𝜑 → 𝐴 ∈ ℕ0) |
| Ref | Expression |
|---|---|
| nn0ge0d | ⊢ (𝜑 → 0 ≤ 𝐴) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nn0red.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℕ0) | |
| 2 | nn0ge0 12551 | . 2 ⊢ (𝐴 ∈ ℕ0 → 0 ≤ 𝐴) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 0 ≤ 𝐴) |
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