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Mirrors > Home > QLE Home > Th. List > ka4ot | Unicode version |
Description: 3-variable version of weakly orthomodular law. It is proved from a weaker-looking equivalent, wom2 434, which in turn is proved from ax-wom 361. |
Ref | Expression |
---|---|
ka4ot |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | le1 146 | . 2 | |
2 | wom2 434 | . . . . . 6 | |
3 | wom2 434 | . . . . . . 7 | |
4 | bicom 96 | . . . . . . . . 9 | |
5 | 4 | ax-r4 37 | . . . . . . . 8 |
6 | bicom 96 | . . . . . . . 8 | |
7 | 5, 6 | 2or 72 | . . . . . . 7 |
8 | 3, 7 | lbtr 139 | . . . . . 6 |
9 | 2, 8 | le2or 168 | . . . . 5 |
10 | oridm 110 | . . . . 5 | |
11 | 9, 10 | lbtr 139 | . . . 4 |
12 | 11 | leror 152 | . . 3 |
13 | ka4lemo 228 | . . 3 | |
14 | ax-a3 32 | . . . 4 | |
15 | oridm 110 | . . . . 5 | |
16 | 15 | lor 70 | . . . 4 |
17 | 14, 16 | ax-r2 36 | . . 3 |
18 | 12, 13, 17 | le3tr2 141 | . 2 |
19 | 1, 18 | lebi 145 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 tb 5 wo 6 wt 8 |
This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-a3 32 ax-a4 33 ax-a5 34 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38 ax-wom 361 |
This theorem depends on definitions: df-b 39 df-a 40 df-t 41 df-f 42 df-i1 44 df-i2 45 df-le 129 df-le1 130 df-le2 131 df-cmtr 134 |
This theorem is referenced by: i3or 497 |
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