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Mirrors > Home > MPE Home > Th. List > df-cntz | Structured version Visualization version Unicode version |
Description: Define the centralizer of a subset of a magma, which is the set of elements each of which commutes with each element of the given subset. (Contributed by Stefan O'Rear, 5-Sep-2015.) |
Ref | Expression |
---|---|
df-cntz |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccntz 17047 |
. 2
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2 | vm |
. . 3
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3 | cvv 3031 |
. . 3
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4 | vs |
. . . 4
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5 | 2 | cv 1451 |
. . . . . 6
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6 | cbs 15199 |
. . . . . 6
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7 | 5, 6 | cfv 5589 |
. . . . 5
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8 | 7 | cpw 3942 |
. . . 4
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9 | vx |
. . . . . . . . 9
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10 | 9 | cv 1451 |
. . . . . . . 8
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11 | vy |
. . . . . . . . 9
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12 | 11 | cv 1451 |
. . . . . . . 8
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13 | cplusg 15268 |
. . . . . . . . 9
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14 | 5, 13 | cfv 5589 |
. . . . . . . 8
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15 | 10, 12, 14 | co 6308 |
. . . . . . 7
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16 | 12, 10, 14 | co 6308 |
. . . . . . 7
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17 | 15, 16 | wceq 1452 |
. . . . . 6
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18 | 4 | cv 1451 |
. . . . . 6
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19 | 17, 11, 18 | wral 2756 |
. . . . 5
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20 | 19, 9, 7 | crab 2760 |
. . . 4
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21 | 4, 8, 20 | cmpt 4454 |
. . 3
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22 | 2, 3, 21 | cmpt 4454 |
. 2
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23 | 1, 22 | wceq 1452 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: cntzfval 17052 |
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