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Definition df-mulg 15318
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 15192 . 2
2 vg . . 3
3 cvv 3006 . . 3
4 vn . . . 4
5 vx . . . 4
6 cz 10453 . . . 4
72cv 1661 . . . . 5
8 cbs 13960 . . . . 5
97, 8cfv 5417 . . . 4
104cv 1661 . . . . . 6
11 cc0 9104 . . . . . 6
1210, 11wceq 1662 . . . . 5
13 c0g 14214 . . . . . 6
147, 13cfv 5417 . . . . 5
15 vs . . . . . 6
16 cplusg 14020 . . . . . . . 8
177, 16cfv 5417 . . . . . . 7
18 cn 10131 . . . . . . . 8
195cv 1661 . . . . . . . . 9
2019csn 3894 . . . . . . . 8
2118, 20cxp 4842 . . . . . . 7
22 c1 9105 . . . . . . 7
2317, 21, 22cseq 11598 . . . . . 6
24 clt 9240 . . . . . . . 8
2511, 10, 24wbr 4302 . . . . . . 7
2615cv 1661 . . . . . . . 8
2710, 26cfv 5417 . . . . . . 7
2810cneg 9416 . . . . . . . . 9
2928, 26cfv 5417 . . . . . . . 8
30 cminusg 15189 . . . . . . . . 9
317, 30cfv 5417 . . . . . . . 8
3229, 31cfv 5417 . . . . . . 7
3325, 27, 32cif 3812 . . . . . 6
3415, 23, 33csb 3313 . . . . 5
3512, 14, 34cif 3812 . . . 4
364, 5, 6, 9, 35cmpt2 6069 . . 3
372, 3, 36cmpt 4360 . 2
381, 37wceq 1662 1
Colors of variables: wff set class
This definition is referenced by:  mulgfval  15394
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