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Mirrors > Home > MPE Home > Th. List > df-limc | Structured version Visualization version Unicode version |
Description: Define the set of limits of a complex function at a point. Under normal circumstances, this will be a singleton or empty, depending on whether the limit exists. (Contributed by Mario Carneiro, 24-Dec-2016.) |
Ref | Expression |
---|---|
df-limc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | climc 22810 |
. 2
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2 | vf |
. . 3
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3 | vx |
. . 3
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4 | cc 9534 |
. . . 4
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5 | cpm 7470 |
. . . 4
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6 | 4, 4, 5 | co 6288 |
. . 3
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7 | vz |
. . . . . . 7
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8 | 2 | cv 1442 |
. . . . . . . . 9
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9 | 8 | cdm 4833 |
. . . . . . . 8
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10 | 3 | cv 1442 |
. . . . . . . . 9
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11 | 10 | csn 3967 |
. . . . . . . 8
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12 | 9, 11 | cun 3401 |
. . . . . . 7
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13 | 7, 3 | weq 1790 |
. . . . . . . 8
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14 | vy |
. . . . . . . . 9
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15 | 14 | cv 1442 |
. . . . . . . 8
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16 | 7 | cv 1442 |
. . . . . . . . 9
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17 | 16, 8 | cfv 5581 |
. . . . . . . 8
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18 | 13, 15, 17 | cif 3880 |
. . . . . . 7
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19 | 7, 12, 18 | cmpt 4460 |
. . . . . 6
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20 | vj |
. . . . . . . . . 10
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21 | 20 | cv 1442 |
. . . . . . . . 9
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22 | crest 15312 |
. . . . . . . . 9
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23 | 21, 12, 22 | co 6288 |
. . . . . . . 8
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24 | ccnp 20234 |
. . . . . . . 8
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25 | 23, 21, 24 | co 6288 |
. . . . . . 7
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26 | 10, 25 | cfv 5581 |
. . . . . 6
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27 | 19, 26 | wcel 1886 |
. . . . 5
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28 | ccnfld 18963 |
. . . . . 6
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29 | ctopn 15313 |
. . . . . 6
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30 | 28, 29 | cfv 5581 |
. . . . 5
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31 | 27, 20, 30 | wsbc 3266 |
. . . 4
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32 | 31, 14 | cab 2436 |
. . 3
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33 | 2, 3, 6, 4, 32 | cmpt2 6290 |
. 2
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34 | 1, 33 | wceq 1443 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: limcfval 22820 limcrcl 22822 |
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