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Mirrors > Home > QLE Home > Th. List > i3lem1 | Unicode version |
Description: Lemma for Kalmbach implication. |
Ref | Expression |
---|---|
i3lem.1 |
Ref | Expression |
---|---|
i3lem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coman1 185 | . . . . . . 7 | |
2 | 1 | comcom 453 | . . . . . 6 |
3 | comorr 184 | . . . . . . 7 | |
4 | comorr 184 | . . . . . . . 8 | |
5 | 4 | comcom3 454 | . . . . . . 7 |
6 | 3, 5 | com2an 484 | . . . . . 6 |
7 | 2, 6 | fh1 469 | . . . . 5 |
8 | anass 76 | . . . . . . . . 9 | |
9 | 8 | ax-r1 35 | . . . . . . . 8 |
10 | anidm 111 | . . . . . . . . 9 | |
11 | 10 | ran 78 | . . . . . . . 8 |
12 | 9, 11 | ax-r2 36 | . . . . . . 7 |
13 | anass 76 | . . . . . . . . 9 | |
14 | 13 | ax-r1 35 | . . . . . . . 8 |
15 | anabs 121 | . . . . . . . . . 10 | |
16 | 15 | ran 78 | . . . . . . . . 9 |
17 | omlan 448 | . . . . . . . . 9 | |
18 | 16, 17 | ax-r2 36 | . . . . . . . 8 |
19 | 14, 18 | ax-r2 36 | . . . . . . 7 |
20 | 12, 19 | 2or 72 | . . . . . 6 |
21 | ax-a2 31 | . . . . . 6 | |
22 | 20, 21 | ax-r2 36 | . . . . 5 |
23 | 7, 22 | ax-r2 36 | . . . 4 |
24 | 23 | ax-r1 35 | . . 3 |
25 | df2i3 498 | . . . . . 6 | |
26 | 25 | ax-r1 35 | . . . . 5 |
27 | i3lem.1 | . . . . 5 | |
28 | 26, 27 | ax-r2 36 | . . . 4 |
29 | 28 | lan 77 | . . 3 |
30 | 24, 29 | ax-r2 36 | . 2 |
31 | an1 106 | . 2 | |
32 | 30, 31 | ax-r2 36 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 wt 8 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: i3lem2 505 i3lem3 506 i3lem4 507 |
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