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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 12358 | . 2 ⊢ ℕ0 = {𝑘 ∈ ℤ ∣ 0 ≤ 𝑘} | |
2 | 0z 12339 | . . 3 ⊢ 0 ∈ ℤ | |
3 | uzval 12593 | . . 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 2770 | 1 ⊢ ℕ0 = (ℤ≥‘0) |
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