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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-edring | Structured version Visualization version Unicode version |
Description: Define division ring on trace-preserving endomorphisms. The multiplication operation is reversed composition, per the definition of E of [Crawley] p. 117, 4th line from bottom. (Contributed by NM, 8-Jun-2013.) |
Ref | Expression |
---|---|
df-edring |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cedring 36041 | . 2 | |
2 | vk | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vw | . . . 4 | |
5 | 2 | cv 1482 | . . . . 5 |
6 | clh 35270 | . . . . 5 | |
7 | 5, 6 | cfv 5888 | . . . 4 |
8 | cnx 15854 | . . . . . . 7 | |
9 | cbs 15857 | . . . . . . 7 | |
10 | 8, 9 | cfv 5888 | . . . . . 6 |
11 | 4 | cv 1482 | . . . . . . 7 |
12 | ctendo 36040 | . . . . . . . 8 | |
13 | 5, 12 | cfv 5888 | . . . . . . 7 |
14 | 11, 13 | cfv 5888 | . . . . . 6 |
15 | 10, 14 | cop 4183 | . . . . 5 |
16 | cplusg 15941 | . . . . . . 7 | |
17 | 8, 16 | cfv 5888 | . . . . . 6 |
18 | vs | . . . . . . 7 | |
19 | vt | . . . . . . 7 | |
20 | vf | . . . . . . . 8 | |
21 | cltrn 35387 | . . . . . . . . . 10 | |
22 | 5, 21 | cfv 5888 | . . . . . . . . 9 |
23 | 11, 22 | cfv 5888 | . . . . . . . 8 |
24 | 20 | cv 1482 | . . . . . . . . . 10 |
25 | 18 | cv 1482 | . . . . . . . . . 10 |
26 | 24, 25 | cfv 5888 | . . . . . . . . 9 |
27 | 19 | cv 1482 | . . . . . . . . . 10 |
28 | 24, 27 | cfv 5888 | . . . . . . . . 9 |
29 | 26, 28 | ccom 5118 | . . . . . . . 8 |
30 | 20, 23, 29 | cmpt 4729 | . . . . . . 7 |
31 | 18, 19, 14, 14, 30 | cmpt2 6652 | . . . . . 6 |
32 | 17, 31 | cop 4183 | . . . . 5 |
33 | cmulr 15942 | . . . . . . 7 | |
34 | 8, 33 | cfv 5888 | . . . . . 6 |
35 | 25, 27 | ccom 5118 | . . . . . . 7 |
36 | 18, 19, 14, 14, 35 | cmpt2 6652 | . . . . . 6 |
37 | 34, 36 | cop 4183 | . . . . 5 |
38 | 15, 32, 37 | ctp 4181 | . . . 4 |
39 | 4, 7, 38 | cmpt 4729 | . . 3 |
40 | 2, 3, 39 | cmpt 4729 | . 2 |
41 | 1, 40 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: erngfset 36087 |
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