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Mirrors > Home > ILE Home > Th. List > df-mulg | 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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmg 12983 |
. 2
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2 | vg |
. . 3
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3 | cvv 2738 |
. . 3
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4 | vn |
. . . 4
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5 | vx |
. . . 4
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6 | cz 9253 |
. . . 4
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7 | 2 | cv 1352 |
. . . . 5
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8 | cbs 12462 |
. . . . 5
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9 | 7, 8 | cfv 5217 |
. . . 4
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10 | 4 | cv 1352 |
. . . . . 6
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11 | cc0 7811 |
. . . . . 6
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12 | 10, 11 | wceq 1353 |
. . . . 5
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13 | c0g 12705 |
. . . . . 6
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14 | 7, 13 | cfv 5217 |
. . . . 5
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15 | vs |
. . . . . 6
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16 | cplusg 12536 |
. . . . . . . 8
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17 | 7, 16 | cfv 5217 |
. . . . . . 7
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18 | cn 8919 |
. . . . . . . 8
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19 | 5 | cv 1352 |
. . . . . . . . 9
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20 | 19 | csn 3593 |
. . . . . . . 8
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21 | 18, 20 | cxp 4625 |
. . . . . . 7
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22 | c1 7812 |
. . . . . . 7
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23 | 17, 21, 22 | cseq 10445 |
. . . . . 6
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24 | clt 7992 |
. . . . . . . 8
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25 | 11, 10, 24 | wbr 4004 |
. . . . . . 7
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26 | 15 | cv 1352 |
. . . . . . . 8
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27 | 10, 26 | cfv 5217 |
. . . . . . 7
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28 | 10 | cneg 8129 |
. . . . . . . . 9
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29 | 28, 26 | cfv 5217 |
. . . . . . . 8
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30 | cminusg 12878 |
. . . . . . . . 9
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31 | 7, 30 | cfv 5217 |
. . . . . . . 8
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32 | 29, 31 | cfv 5217 |
. . . . . . 7
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33 | 25, 27, 32 | cif 3535 |
. . . . . 6
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34 | 15, 23, 33 | csb 3058 |
. . . . 5
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35 | 12, 14, 34 | cif 3535 |
. . . 4
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36 | 4, 5, 6, 9, 35 | cmpo 5877 |
. . 3
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37 | 2, 3, 36 | cmpt 4065 |
. 2
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38 | 1, 37 | wceq 1353 |
1
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Colors of variables: wff set class |
This definition is referenced by: mulgfvalg 12985 |
Copyright terms: Public domain | W3C validator |