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Mirrors > Home > MPE Home > Th. List > df-odz | Structured version Visualization version Unicode version |
Description: Define the order function on the class of integers mod N. (Contributed by Mario Carneiro, 23-Feb-2014.) (Revised by AV, 26-Sep-2020.) |
Ref | Expression |
---|---|
df-odz | inf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | codz 15468 | . 2 | |
2 | vn | . . 3 | |
3 | cn 11020 | . . 3 | |
4 | vx | . . . 4 | |
5 | 4 | cv 1482 | . . . . . . 7 |
6 | 2 | cv 1482 | . . . . . . 7 |
7 | cgcd 15216 | . . . . . . 7 | |
8 | 5, 6, 7 | co 6650 | . . . . . 6 |
9 | c1 9937 | . . . . . 6 | |
10 | 8, 9 | wceq 1483 | . . . . 5 |
11 | cz 11377 | . . . . 5 | |
12 | 10, 4, 11 | crab 2916 | . . . 4 |
13 | vm | . . . . . . . . . 10 | |
14 | 13 | cv 1482 | . . . . . . . . 9 |
15 | cexp 12860 | . . . . . . . . 9 | |
16 | 5, 14, 15 | co 6650 | . . . . . . . 8 |
17 | cmin 10266 | . . . . . . . 8 | |
18 | 16, 9, 17 | co 6650 | . . . . . . 7 |
19 | cdvds 14983 | . . . . . . 7 | |
20 | 6, 18, 19 | wbr 4653 | . . . . . 6 |
21 | 20, 13, 3 | crab 2916 | . . . . 5 |
22 | cr 9935 | . . . . 5 | |
23 | clt 10074 | . . . . 5 | |
24 | 21, 22, 23 | cinf 8347 | . . . 4 inf |
25 | 4, 12, 24 | cmpt 4729 | . . 3 inf |
26 | 2, 3, 25 | cmpt 4729 | . 2 inf |
27 | 1, 26 | wceq 1483 | 1 inf |
Colors of variables: wff setvar class |
This definition is referenced by: odzval 15496 |
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