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Mirrors > Home > ILE Home > Th. List > df-odz | Unicode version |
Description: Define the order function on the class of integers modulo 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 12151 | . 2 | |
2 | vn | . . 3 | |
3 | cn 8867 | . . 3 | |
4 | vx | . . . 4 | |
5 | 4 | cv 1347 | . . . . . . 7 |
6 | 2 | cv 1347 | . . . . . . 7 |
7 | cgcd 11886 | . . . . . . 7 | |
8 | 5, 6, 7 | co 5851 | . . . . . 6 |
9 | c1 7764 | . . . . . 6 | |
10 | 8, 9 | wceq 1348 | . . . . 5 |
11 | cz 9201 | . . . . 5 | |
12 | 10, 4, 11 | crab 2452 | . . . 4 |
13 | vm | . . . . . . . . . 10 | |
14 | 13 | cv 1347 | . . . . . . . . 9 |
15 | cexp 10464 | . . . . . . . . 9 | |
16 | 5, 14, 15 | co 5851 | . . . . . . . 8 |
17 | cmin 8079 | . . . . . . . 8 | |
18 | 16, 9, 17 | co 5851 | . . . . . . 7 |
19 | cdvds 11738 | . . . . . . 7 | |
20 | 6, 18, 19 | wbr 3987 | . . . . . 6 |
21 | 20, 13, 3 | crab 2452 | . . . . 5 |
22 | cr 7762 | . . . . 5 | |
23 | clt 7943 | . . . . 5 | |
24 | 21, 22, 23 | cinf 6957 | . . . 4 inf |
25 | 4, 12, 24 | cmpt 4048 | . . 3 inf |
26 | 2, 3, 25 | cmpt 4048 | . 2 inf |
27 | 1, 26 | wceq 1348 | 1 inf |
Colors of variables: wff set class |
This definition is referenced by: odzval 12184 |
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