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Mirrors > Home > MPE Home > Th. List > df-eqg | Structured version Visualization version Unicode version |
Description: Define the equivalence relation in a quotient ring or quotient group (where is a two-sided ideal or a normal subgroup). For non-normal subgroups this generates the left cosets. (Contributed by Mario Carneiro, 15-Jun-2015.) |
Ref | Expression |
---|---|
df-eqg | ~QG |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cqg 17590 | . 2 ~QG | |
2 | vr | . . 3 | |
3 | vi | . . 3 | |
4 | cvv 3200 | . . 3 | |
5 | vx | . . . . . . . 8 | |
6 | 5 | cv 1482 | . . . . . . 7 |
7 | vy | . . . . . . . 8 | |
8 | 7 | cv 1482 | . . . . . . 7 |
9 | 6, 8 | cpr 4179 | . . . . . 6 |
10 | 2 | cv 1482 | . . . . . . 7 |
11 | cbs 15857 | . . . . . . 7 | |
12 | 10, 11 | cfv 5888 | . . . . . 6 |
13 | 9, 12 | wss 3574 | . . . . 5 |
14 | cminusg 17423 | . . . . . . . . 9 | |
15 | 10, 14 | cfv 5888 | . . . . . . . 8 |
16 | 6, 15 | cfv 5888 | . . . . . . 7 |
17 | cplusg 15941 | . . . . . . . 8 | |
18 | 10, 17 | cfv 5888 | . . . . . . 7 |
19 | 16, 8, 18 | co 6650 | . . . . . 6 |
20 | 3 | cv 1482 | . . . . . 6 |
21 | 19, 20 | wcel 1990 | . . . . 5 |
22 | 13, 21 | wa 384 | . . . 4 |
23 | 22, 5, 7 | copab 4712 | . . 3 |
24 | 2, 3, 4, 4, 23 | cmpt2 6652 | . 2 |
25 | 1, 24 | wceq 1483 | 1 ~QG |
Colors of variables: wff setvar class |
This definition is referenced by: releqg 17641 eqgfval 17642 |
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