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| Mirrors > Home > MPE Home > Th. List > 0nn0 | Structured version Visualization version GIF version | ||
| Description: 0 is a nonnegative integer. (Contributed by Raph Levien, 10-Dec-2002.) |
| Ref | Expression |
|---|---|
| 0nn0 | ⊢ 0 ∈ ℕ0 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqid 2737 | . 2 ⊢ 0 = 0 | |
| 2 | elnn0 12528 | . . . 4 ⊢ (0 ∈ ℕ0 ↔ (0 ∈ ℕ ∨ 0 = 0)) | |
| 3 | 2 | biimpri 228 | . . 3 ⊢ ((0 ∈ ℕ ∨ 0 = 0) → 0 ∈ ℕ0) |
| 4 | 3 | olcs 877 | . 2 ⊢ (0 = 0 → 0 ∈ ℕ0) |
| 5 | 1, 4 | ax-mp 5 | 1 ⊢ 0 ∈ ℕ0 |
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