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Mirrors > Home > QLE Home > Th. List > k1-3 | Unicode version |
Description: Statement (3) in proof of Theorem 1 of Kalmbach, Orthomodular Lattices, p. 21. |
Ref | Expression |
---|---|
k1-3.1 | |
k1-3.2 | |
k1-3.3 |
Ref | Expression |
---|---|
k1-3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | k1-3.1 | . . . . 5 | |
2 | k1-3.2 | . . . . 5 | |
3 | 1, 2 | 2or 72 | . . . 4 |
4 | or4 84 | . . . 4 | |
5 | 3, 4 | ax-r2 36 | . . 3 |
6 | 5 | ran 78 | . 2 |
7 | k1-3.3 | . . . 4 | |
8 | lear 161 | . . . . 5 | |
9 | lear 161 | . . . . 5 | |
10 | 8, 9 | lel2or 170 | . . . 4 |
11 | lear 161 | . . . . 5 | |
12 | lear 161 | . . . . 5 | |
13 | 11, 12 | lel2or 170 | . . . 4 |
14 | 7, 10, 13 | k1-8b 356 | . . 3 |
15 | 14 | ax-r1 35 | . 2 |
16 | 6, 15 | tr 62 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 |
This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-a3 32 ax-a5 34 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38 |
This theorem depends on definitions: df-a 40 df-t 41 df-f 42 df-le1 130 df-le2 131 |
This theorem is referenced by: (None) |
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