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Mirrors > Home > MPE Home > Th. List > df-n0 | Structured version Visualization version 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 11169 | . 2 class ℕ0 | |
2 | cn 10897 | . . 3 class ℕ | |
3 | cc0 9815 | . . . 4 class 0 | |
4 | 3 | csn 4125 | . . 3 class {0} |
5 | 2, 4 | cun 3538 | . 2 class (ℕ ∪ {0}) |
6 | 1, 5 | wceq 1475 | 1 wff ℕ0 = (ℕ ∪ {0}) |
Colors of variables: wff setvar class |
This definition is referenced by: elnn0 11171 nnssnn0 11172 nn0ssre 11173 nn0ex 11175 dfn2 11182 nn0addcl 11205 nn0mulcl 11206 nn0ssz 11275 dvdsprmpweqnn 15427 cply1coe0bi 19491 m2cpminvid2lem 20378 pmatcollpw3fi1 20412 dfrtrcl4 37049 corcltrcl 37050 cotrclrcl 37053 |
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