Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > df-n0 | GIF version |
Description: Define the set of nonnegative integers. (Contributed by Raph Levien, 10-Dec-2002.) |
Ref | Expression |
---|---|
df-n0 | ⊢ ℕ0 = (ℕ ∪ {0}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cn0 9135 | . 2 class ℕ0 | |
2 | cn 8878 | . . 3 class ℕ | |
3 | cc0 7774 | . . . 4 class 0 | |
4 | 3 | csn 3583 | . . 3 class {0} |
5 | 2, 4 | cun 3119 | . 2 class (ℕ ∪ {0}) |
6 | 1, 5 | wceq 1348 | 1 wff ℕ0 = (ℕ ∪ {0}) |
Colors of variables: wff set class |
This definition is referenced by: elnn0 9137 nnssnn0 9138 nn0ssre 9139 nn0ex 9141 dfn2 9148 nn0addcl 9170 nn0mulcl 9171 nn0ssz 9230 dvdsprmpweqnn 12289 |
Copyright terms: Public domain | W3C validator |