Description: Orthocomplement of orthoposet unit. (Contributed by NM, 24-Jan-2012)
Ref | Expression | ||
---|---|---|---|
Hypotheses | opoc1.z | |
|
opoc1.u | |
||
opoc1.o | |
||
Assertion | opoc1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opoc1.z | |
|
2 | opoc1.u | |
|
3 | opoc1.o | |
|
4 | eqid | |
|
5 | 4 1 | op0cl | |
6 | 4 3 | opoccl | |
7 | 5 6 | mpdan | |
8 | eqid | |
|
9 | 4 8 2 | ople1 | |
10 | 7 9 | mpdan | |
11 | 4 2 | op1cl | |
12 | 4 8 3 | oplecon1b | |
13 | 11 5 12 | mpd3an23 | |
14 | 10 13 | mpbird | |
15 | 4 3 | opoccl | |
16 | 11 15 | mpdan | |
17 | 4 8 1 | ople0 | |
18 | 16 17 | mpdan | |
19 | 14 18 | mpbid | |