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Mirrors > Home > MPE Home > Th. List > df-dvds | Unicode version |
Description: Define the divides relation. (Contributed by Paul Chapman, 21-Mar-2011.) |
Ref | Expression |
---|---|
df-dvds |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdvds 13986 | . 2 | |
2 | vx | . . . . . . 7 | |
3 | 2 | cv 1394 | . . . . . 6 |
4 | cz 10889 | . . . . . 6 | |
5 | 3, 4 | wcel 1818 | . . . . 5 |
6 | vy | . . . . . . 7 | |
7 | 6 | cv 1394 | . . . . . 6 |
8 | 7, 4 | wcel 1818 | . . . . 5 |
9 | 5, 8 | wa 369 | . . . 4 |
10 | vn | . . . . . . . 8 | |
11 | 10 | cv 1394 | . . . . . . 7 |
12 | cmul 9518 | . . . . . . 7 | |
13 | 11, 3, 12 | co 6296 | . . . . . 6 |
14 | 13, 7 | wceq 1395 | . . . . 5 |
15 | 14, 10, 4 | wrex 2808 | . . . 4 |
16 | 9, 15 | wa 369 | . . 3 |
17 | 16, 2, 6 | copab 4509 | . 2 |
18 | 1, 17 | wceq 1395 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: divides 13988 dvdszrcl 13991 dvdsrzring 18507 dvdsrz 18508 reldvds 31220 |
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