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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 8935 | . 2 class ℕ0 | |
2 | cn 8684 | . . 3 class ℕ | |
3 | cc0 7588 | . . . 4 class 0 | |
4 | 3 | csn 3497 | . . 3 class {0} |
5 | 2, 4 | cun 3039 | . 2 class (ℕ ∪ {0}) |
6 | 1, 5 | wceq 1316 | 1 wff ℕ0 = (ℕ ∪ {0}) |
Colors of variables: wff set class |
This definition is referenced by: elnn0 8937 nnssnn0 8938 nn0ssre 8939 nn0ex 8941 dfn2 8948 nn0addcl 8970 nn0mulcl 8971 nn0ssz 9030 |
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