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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 | lim ℂfld ↾t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | climc 23626 | . 2 lim | |
2 | vf | . . 3 | |
3 | vx | . . 3 | |
4 | cc 9934 | . . . 4 | |
5 | cpm 7858 | . . . 4 | |
6 | 4, 4, 5 | co 6650 | . . 3 |
7 | vz | . . . . . . 7 | |
8 | 2 | cv 1482 | . . . . . . . . 9 |
9 | 8 | cdm 5114 | . . . . . . . 8 |
10 | 3 | cv 1482 | . . . . . . . . 9 |
11 | 10 | csn 4177 | . . . . . . . 8 |
12 | 9, 11 | cun 3572 | . . . . . . 7 |
13 | 7, 3 | weq 1874 | . . . . . . . 8 |
14 | vy | . . . . . . . . 9 | |
15 | 14 | cv 1482 | . . . . . . . 8 |
16 | 7 | cv 1482 | . . . . . . . . 9 |
17 | 16, 8 | cfv 5888 | . . . . . . . 8 |
18 | 13, 15, 17 | cif 4086 | . . . . . . 7 |
19 | 7, 12, 18 | cmpt 4729 | . . . . . 6 |
20 | vj | . . . . . . . . . 10 | |
21 | 20 | cv 1482 | . . . . . . . . 9 |
22 | crest 16081 | . . . . . . . . 9 ↾t | |
23 | 21, 12, 22 | co 6650 | . . . . . . . 8 ↾t |
24 | ccnp 21029 | . . . . . . . 8 | |
25 | 23, 21, 24 | co 6650 | . . . . . . 7 ↾t |
26 | 10, 25 | cfv 5888 | . . . . . 6 ↾t |
27 | 19, 26 | wcel 1990 | . . . . 5 ↾t |
28 | ccnfld 19746 | . . . . . 6 ℂfld | |
29 | ctopn 16082 | . . . . . 6 | |
30 | 28, 29 | cfv 5888 | . . . . 5 ℂfld |
31 | 27, 20, 30 | wsbc 3435 | . . . 4 ℂfld ↾t |
32 | 31, 14 | cab 2608 | . . 3 ℂfld ↾t |
33 | 2, 3, 6, 4, 32 | cmpt2 6652 | . 2 ℂfld ↾t |
34 | 1, 33 | wceq 1483 | 1 lim ℂfld ↾t |
Colors of variables: wff setvar class |
This definition is referenced by: limcfval 23636 limcrcl 23638 |
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