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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 11330 | . 2 class ℕ0 | |
2 | cn 11058 | . . 3 class ℕ | |
3 | cc0 9974 | . . . 4 class 0 | |
4 | 3 | csn 4210 | . . 3 class {0} |
5 | 2, 4 | cun 3605 | . 2 class (ℕ ∪ {0}) |
6 | 1, 5 | wceq 1523 | 1 wff ℕ0 = (ℕ ∪ {0}) |
Colors of variables: wff setvar class |
This definition is referenced by: elnn0 11332 nnssnn0 11333 nn0ssre 11334 nn0ex 11336 dfn2 11343 nn0addcl 11366 nn0mulcl 11367 nn0ssz 11436 dvdsprmpweqnn 15636 cply1coe0bi 19718 m2cpminvid2lem 20607 pmatcollpw3fi1 20641 dfrtrcl4 38347 corcltrcl 38348 cotrclrcl 38351 |
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