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| Mirrors > Home > MPE Home > Th. List > nn0uz | Structured version Visualization version GIF version | ||
| Description: Nonnegative integers expressed as an upper set of integers. (Contributed by NM, 2-Sep-2005.) |
| Ref | Expression |
|---|---|
| nn0uz | ⊢ ℕ0 = (ℤ≥‘0) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nn0zrab 12646 | . 2 ⊢ ℕ0 = {𝑘 ∈ ℤ ∣ 0 ≤ 𝑘} | |
| 2 | 0z 12624 | . . 3 ⊢ 0 ∈ ℤ | |
| 3 | uzval 12880 | . . 3 ⊢ (0 ∈ ℤ → (ℤ≥‘0) = {𝑘 ∈ ℤ ∣ 0 ≤ 𝑘}) | |
| 4 | 2, 3 | ax-mp 5 | . 2 ⊢ (ℤ≥‘0) = {𝑘 ∈ ℤ ∣ 0 ≤ 𝑘} |
| 5 | 1, 4 | eqtr4i 2768 | 1 ⊢ ℕ0 = (ℤ≥‘0) |
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