Description: Define the set of nonnegative integers. (Contributed by Raph Levien, 10-Dec-2002)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-n0 | ⊢ ℕ0 = ( ℕ ∪ { 0 } ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cn0 | ⊢ ℕ0 | |
| 1 | cn | ⊢ ℕ | |
| 2 | cc0 | ⊢ 0 | |
| 3 | 2 | csn | ⊢ { 0 } |
| 4 | 1 3 | cun | ⊢ ( ℕ ∪ { 0 } ) |
| 5 | 0 4 | wceq | ⊢ ℕ0 = ( ℕ ∪ { 0 } ) |