Description: Contraposition law for orthoposets. ( chsscon3 analog.) (Contributed by NM, 4-Nov-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | opcon3.b | |
|
opcon3.l | |
||
opcon3.o | |
||
Assertion | oplecon3b | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opcon3.b | |
|
2 | opcon3.l | |
|
3 | opcon3.o | |
|
4 | 1 2 3 | oplecon3 | |
5 | simp1 | |
|
6 | 1 3 | opoccl | |
7 | 6 | 3adant2 | |
8 | 1 3 | opoccl | |
9 | 8 | 3adant3 | |
10 | 1 2 3 | oplecon3 | |
11 | 5 7 9 10 | syl3anc | |
12 | 1 3 | opococ | |
13 | 12 | 3adant3 | |
14 | 1 3 | opococ | |
15 | 14 | 3adant2 | |
16 | 13 15 | breq12d | |
17 | 11 16 | sylibd | |
18 | 4 17 | impbid | |