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Mirrors > Home > QLE Home > Th. List > 3vded21 | Unicode version |
Description: A 3-variable theorem. Experiment with weak deduction theorem. |
Ref | Expression |
---|---|
3vded21.1 | |
3vded21.2 |
Ref | Expression |
---|---|
3vded21 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3vded21.2 | . . . . . . 7 | |
2 | df-i0 43 | . . . . . . 7 | |
3 | 1, 2 | lbtr 139 | . . . . . 6 |
4 | 3vded21.1 | . . . . . . 7 | |
5 | df-i0 43 | . . . . . . . 8 | |
6 | 2 | ax-r4 37 | . . . . . . . . 9 |
7 | df-i2 45 | . . . . . . . . . 10 | |
8 | anor3 90 | . . . . . . . . . . 11 | |
9 | 8 | lor 70 | . . . . . . . . . 10 |
10 | 7, 9 | ax-r2 36 | . . . . . . . . 9 |
11 | 6, 10 | 2or 72 | . . . . . . . 8 |
12 | ax-a2 31 | . . . . . . . 8 | |
13 | 5, 11, 12 | 3tr 65 | . . . . . . 7 |
14 | 4, 13 | lbtr 139 | . . . . . 6 |
15 | 3, 14 | ler2an 173 | . . . . 5 |
16 | comor2 462 | . . . . . . . 8 | |
17 | 3 | leror 152 | . . . . . . . . . . . 12 |
18 | ax-a3 32 | . . . . . . . . . . . . 13 | |
19 | oridm 110 | . . . . . . . . . . . . . 14 | |
20 | 19 | lor 70 | . . . . . . . . . . . . 13 |
21 | 18, 20 | ax-r2 36 | . . . . . . . . . . . 12 |
22 | 17, 21 | lbtr 139 | . . . . . . . . . . 11 |
23 | 22 | lecom 180 | . . . . . . . . . 10 |
24 | 23 | comcom 453 | . . . . . . . . 9 |
25 | 24 | comcom2 183 | . . . . . . . 8 |
26 | 16, 25 | com2or 483 | . . . . . . 7 |
27 | comid 187 | . . . . . . . 8 | |
28 | 27 | comcom2 183 | . . . . . . 7 |
29 | 26, 28 | fh1 469 | . . . . . 6 |
30 | or0 102 | . . . . . . 7 | |
31 | 16, 25 | fh1 469 | . . . . . . . . 9 |
32 | 31 | ax-r1 35 | . . . . . . . 8 |
33 | dff 101 | . . . . . . . 8 | |
34 | 32, 33 | 2or 72 | . . . . . . 7 |
35 | ax-a2 31 | . . . . . . . . . 10 | |
36 | 35 | ran 78 | . . . . . . . . 9 |
37 | ancom 74 | . . . . . . . . 9 | |
38 | anabs 121 | . . . . . . . . 9 | |
39 | 36, 37, 38 | 3tr 65 | . . . . . . . 8 |
40 | 39 | ax-r5 38 | . . . . . . 7 |
41 | 30, 34, 40 | 3tr2 64 | . . . . . 6 |
42 | 29, 41 | ax-r2 36 | . . . . 5 |
43 | 15, 42 | lbtr 139 | . . . 4 |
44 | 43 | leran 153 | . . 3 |
45 | anabs 121 | . . 3 | |
46 | comor2 462 | . . . . 5 | |
47 | comid 187 | . . . . . . 7 | |
48 | 47 | comcom2 183 | . . . . . 6 |
49 | 23, 48 | com2an 484 | . . . . 5 |
50 | 46, 49 | fh1r 473 | . . . 4 |
51 | ax-a2 31 | . . . . . . 7 | |
52 | 51 | lan 77 | . . . . . 6 |
53 | anabs 121 | . . . . . 6 | |
54 | 52, 53 | ax-r2 36 | . . . . 5 |
55 | an32 83 | . . . . . 6 | |
56 | anass 76 | . . . . . 6 | |
57 | dff 101 | . . . . . . . . 9 | |
58 | 57 | lan 77 | . . . . . . . 8 |
59 | 58 | ax-r1 35 | . . . . . . 7 |
60 | an0 108 | . . . . . . 7 | |
61 | 59, 60 | ax-r2 36 | . . . . . 6 |
62 | 55, 56, 61 | 3tr 65 | . . . . 5 |
63 | 54, 62 | 2or 72 | . . . 4 |
64 | 50, 63 | ax-r2 36 | . . 3 |
65 | 44, 45, 64 | le3tr2 141 | . 2 |
66 | or0 102 | . 2 | |
67 | 65, 66 | lbtr 139 | 1 |
Colors of variables: term |
Syntax hints: wle 2 wn 4 wo 6 wa 7 wf 9 wi0 11 wi2 13 |
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-i0 43 df-i2 45 df-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: 3vded22 818 |
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