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Mirrors > Home > MPE Home > Th. List > df-od | Structured version Visualization version Unicode version |
Description: Define the order of an element in a group. (Contributed by Mario Carneiro, 13-Jul-2014.) (Revised by Stefan O'Rear, 4-Sep-2015.) (Revised by AV, 5-Oct-2020.) |
Ref | Expression |
---|---|
df-od |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cod 17177 |
. 2
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2 | vg |
. . 3
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3 | cvv 3047 |
. . 3
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4 | vx |
. . . 4
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5 | 2 | cv 1445 |
. . . . 5
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6 | cbs 15133 |
. . . . 5
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7 | 5, 6 | cfv 5585 |
. . . 4
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8 | vi |
. . . . 5
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9 | vn |
. . . . . . . . 9
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10 | 9 | cv 1445 |
. . . . . . . 8
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11 | 4 | cv 1445 |
. . . . . . . 8
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12 | cmg 16684 |
. . . . . . . . 9
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13 | 5, 12 | cfv 5585 |
. . . . . . . 8
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14 | 10, 11, 13 | co 6295 |
. . . . . . 7
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15 | c0g 15350 |
. . . . . . . 8
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16 | 5, 15 | cfv 5585 |
. . . . . . 7
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17 | 14, 16 | wceq 1446 |
. . . . . 6
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18 | cn 10616 |
. . . . . 6
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19 | 17, 9, 18 | crab 2743 |
. . . . 5
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20 | 8 | cv 1445 |
. . . . . . 7
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21 | c0 3733 |
. . . . . . 7
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22 | 20, 21 | wceq 1446 |
. . . . . 6
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23 | cc0 9544 |
. . . . . 6
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24 | cr 9543 |
. . . . . . 7
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25 | clt 9680 |
. . . . . . 7
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26 | 20, 24, 25 | cinf 7960 |
. . . . . 6
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27 | 22, 23, 26 | cif 3883 |
. . . . 5
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28 | 8, 19, 27 | csb 3365 |
. . . 4
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29 | 4, 7, 28 | cmpt 4464 |
. . 3
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30 | 2, 3, 29 | cmpt 4464 |
. 2
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31 | 1, 30 | wceq 1446 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: odfval 17191 |
Copyright terms: Public domain | W3C validator |