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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-siga | Structured version Visualization version Unicode version |
Description: Define a sigma-algebra, i.e. a set closed under complement and countable union. Literature usually uses capital greek sigma and omega letters for the algebra set, and the base set respectively. We are using and as a parallel. (Contributed by Thierry Arnoux, 3-Sep-2016.) |
Ref | Expression |
---|---|
df-siga | sigAlgebra |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csiga 30170 | . 2 sigAlgebra | |
2 | vo | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vs | . . . . . . 7 | |
5 | 4 | cv 1482 | . . . . . 6 |
6 | 2 | cv 1482 | . . . . . . 7 |
7 | 6 | cpw 4158 | . . . . . 6 |
8 | 5, 7 | wss 3574 | . . . . 5 |
9 | 2, 4 | wel 1991 | . . . . . 6 |
10 | vx | . . . . . . . . . 10 | |
11 | 10 | cv 1482 | . . . . . . . . 9 |
12 | 6, 11 | cdif 3571 | . . . . . . . 8 |
13 | 12, 5 | wcel 1990 | . . . . . . 7 |
14 | 13, 10, 5 | wral 2912 | . . . . . 6 |
15 | com 7065 | . . . . . . . . 9 | |
16 | cdom 7953 | . . . . . . . . 9 | |
17 | 11, 15, 16 | wbr 4653 | . . . . . . . 8 |
18 | 11 | cuni 4436 | . . . . . . . . 9 |
19 | 18, 5 | wcel 1990 | . . . . . . . 8 |
20 | 17, 19 | wi 4 | . . . . . . 7 |
21 | 5 | cpw 4158 | . . . . . . 7 |
22 | 20, 10, 21 | wral 2912 | . . . . . 6 |
23 | 9, 14, 22 | w3a 1037 | . . . . 5 |
24 | 8, 23 | wa 384 | . . . 4 |
25 | 24, 4 | cab 2608 | . . 3 |
26 | 2, 3, 25 | cmpt 4729 | . 2 |
27 | 1, 26 | wceq 1483 | 1 sigAlgebra |
Colors of variables: wff setvar class |
This definition is referenced by: sigaval 30173 issiga 30174 isrnsigaOLD 30175 isrnsiga 30176 |
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