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Mirrors > Home > MPE Home > Th. List > df-dvdsr | Structured version Visualization version Unicode version |
Description: Define the (right) divisibility relation in a ring. Access to the left divisibility relation is available through roppr. (Contributed by Mario Carneiro, 1-Dec-2014.) |
Ref | Expression |
---|---|
df-dvdsr | r |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdsr 18638 | . 2 r | |
2 | vw | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vx | . . . . . . 7 | |
5 | 4 | cv 1482 | . . . . . 6 |
6 | 2 | cv 1482 | . . . . . . 7 |
7 | cbs 15857 | . . . . . . 7 | |
8 | 6, 7 | cfv 5888 | . . . . . 6 |
9 | 5, 8 | wcel 1990 | . . . . 5 |
10 | vz | . . . . . . . . 9 | |
11 | 10 | cv 1482 | . . . . . . . 8 |
12 | cmulr 15942 | . . . . . . . . 9 | |
13 | 6, 12 | cfv 5888 | . . . . . . . 8 |
14 | 11, 5, 13 | co 6650 | . . . . . . 7 |
15 | vy | . . . . . . . 8 | |
16 | 15 | cv 1482 | . . . . . . 7 |
17 | 14, 16 | wceq 1483 | . . . . . 6 |
18 | 17, 10, 8 | wrex 2913 | . . . . 5 |
19 | 9, 18 | wa 384 | . . . 4 |
20 | 19, 4, 15 | copab 4712 | . . 3 |
21 | 2, 3, 20 | cmpt 4729 | . 2 |
22 | 1, 21 | wceq 1483 | 1 r |
Colors of variables: wff setvar class |
This definition is referenced by: reldvdsr 18644 dvdsrval 18645 |
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