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| Mirrors > Home > MPE Home > Th. List > nnuz | Structured version Visualization version GIF version | ||
| Description: Positive integers expressed as an upper set of integers. (Contributed by NM, 2-Sep-2005.) |
| Ref | Expression |
|---|---|
| nnuz | ⊢ ℕ = (ℤ≥‘1) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nnzrab 12645 | . 2 ⊢ ℕ = {𝑘 ∈ ℤ ∣ 1 ≤ 𝑘} | |
| 2 | 1z 12647 | . . 3 ⊢ 1 ∈ ℤ | |
| 3 | uzval 12880 | . . 3 ⊢ (1 ∈ ℤ → (ℤ≥‘1) = {𝑘 ∈ ℤ ∣ 1 ≤ 𝑘}) | |
| 4 | 2, 3 | ax-mp 5 | . 2 ⊢ (ℤ≥‘1) = {𝑘 ∈ ℤ ∣ 1 ≤ 𝑘} |
| 5 | 1, 4 | eqtr4i 2768 | 1 ⊢ ℕ = (ℤ≥‘1) |
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