| Metamath Proof Explorer |
< Previous
Next >
Related theorems GIF version |
| Description: Define the set of nonnegative integers. |
| Ref | Expression |
|---|---|
| df-n0 | ⊢ ℕ0 = (ℕ ∪ {0}) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cn0 4094 | . 2 class ℕ0 | |
| 2 | cn 4093 | . . 3 class ℕ | |
| 3 | cc0 4028 | . . . 4 class 0 | |
| 4 | 3 | csn 1808 | . . 3 class {0} |
| 5 | 2, 4 | cun 1485 | . 2 class (ℕ ∪ {0}) |
| 6 | 1, 5 | wceq 1091 | 1 wff ℕ0 = (ℕ ∪ {0}) |
| Colors of variables: wff set class |
| This definition is referenced by: elnn0 4536 nnssnn0 4537 nn0ssre 4538 nn0ssz 4578 |