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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-oposet | Structured version Visualization version Unicode version |
Description: Define the class of orthoposets, which are bounded posets with an orthocomplementation operation. Note that p ) e. dom ( lub means there is an upper bound , and similarly for the element. (Contributed by NM, 20-Oct-2011.) (Revised by NM, 13-Sep-2018.) |
Ref | Expression |
---|---|
df-oposet |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cops 34459 | . 2 | |
2 | vp | . . . . . . . 8 | |
3 | 2 | cv 1482 | . . . . . . 7 |
4 | cbs 15857 | . . . . . . 7 | |
5 | 3, 4 | cfv 5888 | . . . . . 6 |
6 | club 16942 | . . . . . . . 8 | |
7 | 3, 6 | cfv 5888 | . . . . . . 7 |
8 | 7 | cdm 5114 | . . . . . 6 |
9 | 5, 8 | wcel 1990 | . . . . 5 |
10 | cglb 16943 | . . . . . . . 8 | |
11 | 3, 10 | cfv 5888 | . . . . . . 7 |
12 | 11 | cdm 5114 | . . . . . 6 |
13 | 5, 12 | wcel 1990 | . . . . 5 |
14 | 9, 13 | wa 384 | . . . 4 |
15 | vo | . . . . . . . 8 | |
16 | 15 | cv 1482 | . . . . . . 7 |
17 | coc 15949 | . . . . . . . 8 | |
18 | 3, 17 | cfv 5888 | . . . . . . 7 |
19 | 16, 18 | wceq 1483 | . . . . . 6 |
20 | va | . . . . . . . . . . . . 13 | |
21 | 20 | cv 1482 | . . . . . . . . . . . 12 |
22 | 21, 16 | cfv 5888 | . . . . . . . . . . 11 |
23 | 22, 5 | wcel 1990 | . . . . . . . . . 10 |
24 | 22, 16 | cfv 5888 | . . . . . . . . . . 11 |
25 | 24, 21 | wceq 1483 | . . . . . . . . . 10 |
26 | vb | . . . . . . . . . . . . 13 | |
27 | 26 | cv 1482 | . . . . . . . . . . . 12 |
28 | cple 15948 | . . . . . . . . . . . . 13 | |
29 | 3, 28 | cfv 5888 | . . . . . . . . . . . 12 |
30 | 21, 27, 29 | wbr 4653 | . . . . . . . . . . 11 |
31 | 27, 16 | cfv 5888 | . . . . . . . . . . . 12 |
32 | 31, 22, 29 | wbr 4653 | . . . . . . . . . . 11 |
33 | 30, 32 | wi 4 | . . . . . . . . . 10 |
34 | 23, 25, 33 | w3a 1037 | . . . . . . . . 9 |
35 | cjn 16944 | . . . . . . . . . . . 12 | |
36 | 3, 35 | cfv 5888 | . . . . . . . . . . 11 |
37 | 21, 22, 36 | co 6650 | . . . . . . . . . 10 |
38 | cp1 17038 | . . . . . . . . . . 11 | |
39 | 3, 38 | cfv 5888 | . . . . . . . . . 10 |
40 | 37, 39 | wceq 1483 | . . . . . . . . 9 |
41 | cmee 16945 | . . . . . . . . . . . 12 | |
42 | 3, 41 | cfv 5888 | . . . . . . . . . . 11 |
43 | 21, 22, 42 | co 6650 | . . . . . . . . . 10 |
44 | cp0 17037 | . . . . . . . . . . 11 | |
45 | 3, 44 | cfv 5888 | . . . . . . . . . 10 |
46 | 43, 45 | wceq 1483 | . . . . . . . . 9 |
47 | 34, 40, 46 | w3a 1037 | . . . . . . . 8 |
48 | 47, 26, 5 | wral 2912 | . . . . . . 7 |
49 | 48, 20, 5 | wral 2912 | . . . . . 6 |
50 | 19, 49 | wa 384 | . . . . 5 |
51 | 50, 15 | wex 1704 | . . . 4 |
52 | 14, 51 | wa 384 | . . 3 |
53 | cpo 16940 | . . 3 | |
54 | 52, 2, 53 | crab 2916 | . 2 |
55 | 1, 54 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: isopos 34467 |
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