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Mirrors > Home > ILE Home > Th. List > df-odz | Unicode version |
Description: Define the order function on the class of integers modulo N. (Contributed by Mario Carneiro, 23-Feb-2014.) (Revised by AV, 26-Sep-2020.) |
Ref | Expression |
---|---|
df-odz |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | codz 12200 |
. 2
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2 | vn |
. . 3
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3 | cn 8915 |
. . 3
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4 | vx |
. . . 4
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5 | 4 | cv 1352 |
. . . . . . 7
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6 | 2 | cv 1352 |
. . . . . . 7
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7 | cgcd 11935 |
. . . . . . 7
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8 | 5, 6, 7 | co 5872 |
. . . . . 6
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9 | c1 7809 |
. . . . . 6
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10 | 8, 9 | wceq 1353 |
. . . . 5
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11 | cz 9249 |
. . . . 5
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12 | 10, 4, 11 | crab 2459 |
. . . 4
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13 | vm |
. . . . . . . . . 10
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14 | 13 | cv 1352 |
. . . . . . . . 9
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15 | cexp 10514 |
. . . . . . . . 9
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16 | 5, 14, 15 | co 5872 |
. . . . . . . 8
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17 | cmin 8124 |
. . . . . . . 8
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18 | 16, 9, 17 | co 5872 |
. . . . . . 7
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19 | cdvds 11787 |
. . . . . . 7
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20 | 6, 18, 19 | wbr 4002 |
. . . . . 6
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21 | 20, 13, 3 | crab 2459 |
. . . . 5
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22 | cr 7807 |
. . . . 5
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23 | clt 7988 |
. . . . 5
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24 | 21, 22, 23 | cinf 6979 |
. . . 4
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25 | 4, 12, 24 | cmpt 4063 |
. . 3
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26 | 2, 3, 25 | cmpt 4063 |
. 2
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27 | 1, 26 | wceq 1353 |
1
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Colors of variables: wff set class |
This definition is referenced by: odzval 12233 |
Copyright terms: Public domain | W3C validator |