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Mirrors > Home > QLE Home > Th. List > vneulem6 | Unicode version |
Description: Part of von Neumann's lemma. Lemma 9, Kalmbach p. 96 |
Ref | Expression |
---|---|
vneulem6.1 |
Ref | Expression |
---|---|
vneulem6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 73 | . . . . . . 7 | |
2 | 1 | ror 71 | . . . . . 6 |
3 | or32 82 | . . . . . 6 | |
4 | 2, 3 | tr 62 | . . . . 5 |
5 | or32 82 | . . . . 5 | |
6 | 4, 5 | 2an 79 | . . . 4 |
7 | vneulem5 1133 | . . . 4 | |
8 | 6, 7 | ax-r2 36 | . . 3 |
9 | leor 159 | . . . 4 | |
10 | or32 82 | . . . . . . 7 | |
11 | 10 | ran 78 | . . . . . 6 |
12 | ax-a2 31 | . . . . . . . . 9 | |
13 | ax-a2 31 | . . . . . . . . 9 | |
14 | 12, 13 | 2an 79 | . . . . . . . 8 |
15 | vneulem6.1 | . . . . . . . 8 | |
16 | 14, 15 | tr 62 | . . . . . . 7 |
17 | 16 | vneulem4 1132 | . . . . . 6 |
18 | 11, 17 | tr 62 | . . . . 5 |
19 | leao3 164 | . . . . . 6 | |
20 | 19 | lerr 150 | . . . . 5 |
21 | 18, 20 | bltr 138 | . . . 4 |
22 | 9, 21 | lel2or 170 | . . 3 |
23 | 8, 22 | bltr 138 | . 2 |
24 | leao2 163 | . . . . 5 | |
25 | 24 | ler 149 | . . . 4 |
26 | leor 159 | . . . . 5 | |
27 | 26 | leror 152 | . . . 4 |
28 | 25, 27 | lel2or 170 | . . 3 |
29 | leao3 164 | . . . . 5 | |
30 | 29 | ler 149 | . . . 4 |
31 | leo 158 | . . . . 5 | |
32 | 31 | leror 152 | . . . 4 |
33 | 30, 32 | lel2or 170 | . . 3 |
34 | 28, 33 | ler2an 173 | . 2 |
35 | 23, 34 | lebi 145 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wo 6 wa 7 wf 9 |
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 ax-ml 1120 |
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: vneulem8 1136 |
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