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Mirrors > Home > MPE Home > Th. List > df-cau | Structured version Visualization version Unicode version |
Description: Define a function on metric spaces whose value is the set of Cauchy sequences of the space. (Contributed by NM, 8-Sep-2006.) |
Ref | Expression |
---|---|
df-cau |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cca 22278 |
. 2
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2 | vd |
. . 3
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3 | cxmt 19010 |
. . . . 5
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4 | 3 | crn 4857 |
. . . 4
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5 | 4 | cuni 4212 |
. . 3
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6 | vj |
. . . . . . . . 9
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7 | 6 | cv 1454 |
. . . . . . . 8
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8 | cuz 11193 |
. . . . . . . 8
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9 | 7, 8 | cfv 5605 |
. . . . . . 7
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10 | vf |
. . . . . . . . . 10
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11 | 10 | cv 1454 |
. . . . . . . . 9
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12 | 7, 11 | cfv 5605 |
. . . . . . . 8
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13 | vx |
. . . . . . . . 9
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14 | 13 | cv 1454 |
. . . . . . . 8
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15 | 2 | cv 1454 |
. . . . . . . . 9
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16 | cbl 19012 |
. . . . . . . . 9
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17 | 15, 16 | cfv 5605 |
. . . . . . . 8
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18 | 12, 14, 17 | co 6320 |
. . . . . . 7
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19 | 11, 9 | cres 4858 |
. . . . . . 7
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20 | 9, 18, 19 | wf 5601 |
. . . . . 6
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21 | cz 10971 |
. . . . . 6
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22 | 20, 6, 21 | wrex 2750 |
. . . . 5
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23 | crp 11336 |
. . . . 5
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24 | 22, 13, 23 | wral 2749 |
. . . 4
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25 | 15 | cdm 4856 |
. . . . . 6
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26 | 25 | cdm 4856 |
. . . . 5
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27 | cc 9568 |
. . . . 5
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28 | cpm 7504 |
. . . . 5
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29 | 26, 27, 28 | co 6320 |
. . . 4
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30 | 24, 10, 29 | crab 2753 |
. . 3
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31 | 2, 5, 30 | cmpt 4477 |
. 2
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32 | 1, 31 | wceq 1455 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: caufval 22300 |
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