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Mirrors > Home > ILE Home > Th. List > df-0g | Unicode version |
Description: Define group identity element. Remark: this definition is required here because the symbol is already used in df-gsum 12129. The related theorems will be provided later. (Contributed by NM, 20-Aug-2011.) |
Ref | Expression |
---|---|
df-0g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | c0g 12126 | . 2 | |
2 | vg | . . 3 | |
3 | cvv 2681 | . . 3 | |
4 | ve | . . . . . . 7 | |
5 | 4 | cv 1330 | . . . . . 6 |
6 | 2 | cv 1330 | . . . . . . 7 |
7 | cbs 11948 | . . . . . . 7 | |
8 | 6, 7 | cfv 5118 | . . . . . 6 |
9 | 5, 8 | wcel 1480 | . . . . 5 |
10 | vx | . . . . . . . . . 10 | |
11 | 10 | cv 1330 | . . . . . . . . 9 |
12 | cplusg 12010 | . . . . . . . . . 10 | |
13 | 6, 12 | cfv 5118 | . . . . . . . . 9 |
14 | 5, 11, 13 | co 5767 | . . . . . . . 8 |
15 | 14, 11 | wceq 1331 | . . . . . . 7 |
16 | 11, 5, 13 | co 5767 | . . . . . . . 8 |
17 | 16, 11 | wceq 1331 | . . . . . . 7 |
18 | 15, 17 | wa 103 | . . . . . 6 |
19 | 18, 10, 8 | wral 2414 | . . . . 5 |
20 | 9, 19 | wa 103 | . . . 4 |
21 | 20, 4 | cio 5081 | . . 3 |
22 | 2, 3, 21 | cmpt 3984 | . 2 |
23 | 1, 22 | wceq 1331 | 1 |
Colors of variables: wff set class |
This definition is referenced by: (None) |
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