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Mirrors > Home > MPE Home > Th. List > df-mulg | Structured version Visualization version Unicode version |
Description: Define the group multiple function, also known as group exponentiation when viewed multiplicatively. (Contributed by Mario Carneiro, 11-Dec-2014.) |
Ref | Expression |
---|---|
df-mulg | .g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmg 17540 | . 2 .g | |
2 | vg | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vn | . . . 4 | |
5 | vx | . . . 4 | |
6 | cz 11377 | . . . 4 | |
7 | 2 | cv 1482 | . . . . 5 |
8 | cbs 15857 | . . . . 5 | |
9 | 7, 8 | cfv 5888 | . . . 4 |
10 | 4 | cv 1482 | . . . . . 6 |
11 | cc0 9936 | . . . . . 6 | |
12 | 10, 11 | wceq 1483 | . . . . 5 |
13 | c0g 16100 | . . . . . 6 | |
14 | 7, 13 | cfv 5888 | . . . . 5 |
15 | vs | . . . . . 6 | |
16 | cplusg 15941 | . . . . . . . 8 | |
17 | 7, 16 | cfv 5888 | . . . . . . 7 |
18 | cn 11020 | . . . . . . . 8 | |
19 | 5 | cv 1482 | . . . . . . . . 9 |
20 | 19 | csn 4177 | . . . . . . . 8 |
21 | 18, 20 | cxp 5112 | . . . . . . 7 |
22 | c1 9937 | . . . . . . 7 | |
23 | 17, 21, 22 | cseq 12801 | . . . . . 6 |
24 | clt 10074 | . . . . . . . 8 | |
25 | 11, 10, 24 | wbr 4653 | . . . . . . 7 |
26 | 15 | cv 1482 | . . . . . . . 8 |
27 | 10, 26 | cfv 5888 | . . . . . . 7 |
28 | 10 | cneg 10267 | . . . . . . . . 9 |
29 | 28, 26 | cfv 5888 | . . . . . . . 8 |
30 | cminusg 17423 | . . . . . . . . 9 | |
31 | 7, 30 | cfv 5888 | . . . . . . . 8 |
32 | 29, 31 | cfv 5888 | . . . . . . 7 |
33 | 25, 27, 32 | cif 4086 | . . . . . 6 |
34 | 15, 23, 33 | csb 3533 | . . . . 5 |
35 | 12, 14, 34 | cif 4086 | . . . 4 |
36 | 4, 5, 6, 9, 35 | cmpt2 6652 | . . 3 |
37 | 2, 3, 36 | cmpt 4729 | . 2 |
38 | 1, 37 | wceq 1483 | 1 .g |
Colors of variables: wff setvar class |
This definition is referenced by: mulgfval 17542 |
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