MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-mulg Unicode version

Definition df-mulg 15386
Description: Define the group multiple function, also known as group exponentiation when viewed multiplicatively. (Contributed by Mario Carneiro, 11-Dec-2014.)
Assertion
Ref Expression
df-mulg
Distinct variable group:   , , ,

Detailed syntax breakdown of Definition df-mulg
StepHypRef Expression
1 cmg 15255 . 2
2 vg . . 3
3 cvv 3015 . . 3
4 vn . . . 4
5 vx . . . 4
6 cz 10510 . . . 4
72cv 1669 . . . . 5
8 cbs 14021 . . . . 5
97, 8cfv 5438 . . . 4
104cv 1669 . . . . . 6
11 cc0 9161 . . . . . 6
1210, 11wceq 1670 . . . . 5
13 c0g 14277 . . . . . 6
147, 13cfv 5438 . . . . 5
15 vs . . . . . 6
16 cplusg 14083 . . . . . . . 8
177, 16cfv 5438 . . . . . . 7
18 cn 10188 . . . . . . . 8
195cv 1669 . . . . . . . . 9
2019csn 3909 . . . . . . . 8
2118, 20cxp 4860 . . . . . . 7
22 c1 9162 . . . . . . 7
2317, 21, 22cseq 11655 . . . . . 6
24 clt 9297 . . . . . . . 8
2511, 10, 24wbr 4318 . . . . . . 7
2615cv 1669 . . . . . . . 8
2710, 26cfv 5438 . . . . . . 7
2810cneg 9473 . . . . . . . . 9
2928, 26cfv 5438 . . . . . . . 8
30 cminusg 15252 . . . . . . . . 9
317, 30cfv 5438 . . . . . . . 8
3229, 31cfv 5438 . . . . . . 7
3325, 27, 32cif 3825 . . . . . 6
3415, 23, 33csb 3325 . . . . 5
3512, 14, 34cif 3825 . . . 4
364, 5, 6, 9, 35cmpt2 6105 . . 3
372, 3, 36cmpt 4376 . 2
381, 37wceq 1670 1
Colors of variables: wff set class
This definition is referenced by:  mulgfval  15462
  Copyright terms: Public domain W3C validator