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Mirrors > Home > QLE Home > Th. List > i3orlem8 | Unicode version |
Description: Lemma for Kalmbach implication OR builder. |
Ref | Expression |
---|---|
i3orlem8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anass 76 | . . . . . 6 | |
2 | ancom 74 | . . . . . . 7 | |
3 | 2 | lan 77 | . . . . . 6 |
4 | 1, 3 | ax-r2 36 | . . . . 5 |
5 | leor 159 | . . . . 5 | |
6 | 4, 5 | bltr 138 | . . . 4 |
7 | i3n1 249 | . . . . . . 7 | |
8 | 7 | lan 77 | . . . . . 6 |
9 | comor1 461 | . . . . . . . . 9 | |
10 | comor2 462 | . . . . . . . . . 10 | |
11 | 10 | comcom2 183 | . . . . . . . . 9 |
12 | 9, 11 | com2an 484 | . . . . . . . 8 |
13 | 9, 10 | com2an 484 | . . . . . . . 8 |
14 | 12, 13 | com2or 483 | . . . . . . 7 |
15 | 9 | comcom2 183 | . . . . . . . 8 |
16 | 9, 11 | com2or 483 | . . . . . . . 8 |
17 | 15, 16 | com2an 484 | . . . . . . 7 |
18 | 14, 17 | fh1 469 | . . . . . 6 |
19 | 8, 18 | ax-r2 36 | . . . . 5 |
20 | 19 | ax-r1 35 | . . . 4 |
21 | 6, 20 | lbtr 139 | . . 3 |
22 | 21 | ler 149 | . 2 |
23 | i3orlem6 557 | . . 3 | |
24 | 23 | ax-r1 35 | . 2 |
25 | 22, 24 | lbtr 139 | 1 |
Colors of variables: term |
Syntax hints: wle 2 wn 4 wo 6 wa 7 wi3 14 |
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-r3 439 |
This theorem depends on definitions: df-b 39 df-a 40 df-t 41 df-f 42 df-i3 46 df-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: (None) |
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