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Mirrors > Home > MPE Home > Th. List > df-clat | Structured version Visualization version Unicode version |
Description: Define the class of all complete lattices, where every subset of the base set has an LUB and a GLB. (Contributed by NM, 18-Oct-2012.) (Revised by NM, 12-Sep-2018.) |
Ref | Expression |
---|---|
df-clat |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccla 17107 | . 2 | |
2 | vp | . . . . . . . 8 | |
3 | 2 | cv 1482 | . . . . . . 7 |
4 | club 16942 | . . . . . . 7 | |
5 | 3, 4 | cfv 5888 | . . . . . 6 |
6 | 5 | cdm 5114 | . . . . 5 |
7 | cbs 15857 | . . . . . . 7 | |
8 | 3, 7 | cfv 5888 | . . . . . 6 |
9 | 8 | cpw 4158 | . . . . 5 |
10 | 6, 9 | wceq 1483 | . . . 4 |
11 | cglb 16943 | . . . . . . 7 | |
12 | 3, 11 | cfv 5888 | . . . . . 6 |
13 | 12 | cdm 5114 | . . . . 5 |
14 | 13, 9 | wceq 1483 | . . . 4 |
15 | 10, 14 | wa 384 | . . 3 |
16 | cpo 16940 | . . 3 | |
17 | 15, 2, 16 | crab 2916 | . 2 |
18 | 1, 17 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: isclat 17109 |
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