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Mirrors > Home > QLE Home > Th. List > lem4.6.6i1j3 | Unicode version |
Description: Equation 4.14 of [MegPav2000] p. 23. The variable i in the paper is set to 1, and j is set to 3. (Contributed by Roy F. Longton, 3-Jul-05.) |
Ref | Expression |
---|---|
lem4.6.6i1j3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leo 158 | . . . . . . . 8 | |
2 | 1 | ler 149 | . . . . . . 7 |
3 | 2 | lecom 180 | . . . . . 6 |
4 | 3 | comcom6 459 | . . . . 5 |
5 | 4 | comcom 453 | . . . 4 |
6 | lear 161 | . . . . . . 7 | |
7 | 6 | lelor 166 | . . . . . 6 |
8 | lea 160 | . . . . . . . 8 | |
9 | lea 160 | . . . . . . . 8 | |
10 | 8, 9 | lel2or 170 | . . . . . . 7 |
11 | 10 | ler 149 | . . . . . 6 |
12 | 7, 11 | lel2or 170 | . . . . 5 |
13 | 12 | lecom 180 | . . . 4 |
14 | 5, 13 | fh3 471 | . . 3 |
15 | ax-a3 32 | . . 3 | |
16 | ax-a2 31 | . . . . 5 | |
17 | 16 | ran 78 | . . . 4 |
18 | ax-a3 32 | . . . . . 6 | |
19 | 18 | ax-r1 35 | . . . . 5 |
20 | 19 | ran 78 | . . . 4 |
21 | ax-a3 32 | . . . . . . . 8 | |
22 | 21 | ax-r1 35 | . . . . . . 7 |
23 | 22 | ax-r5 38 | . . . . . 6 |
24 | 23 | ran 78 | . . . . 5 |
25 | ax-a4 33 | . . . . . . . . . 10 | |
26 | 25 | df-le1 130 | . . . . . . . . 9 |
27 | 26 | ler 149 | . . . . . . . 8 |
28 | 27 | ler 149 | . . . . . . 7 |
29 | 28 | lem3.3.5lem 1054 | . . . . . 6 |
30 | 29 | ran 78 | . . . . 5 |
31 | an1r 107 | . . . . . 6 | |
32 | ax-a2 31 | . . . . . . 7 | |
33 | 32 | ax-r5 38 | . . . . . 6 |
34 | ax-a3 32 | . . . . . . 7 | |
35 | orordi 112 | . . . . . . . . . 10 | |
36 | 35 | ax-r1 35 | . . . . . . . . 9 |
37 | 36 | lor 70 | . . . . . . . 8 |
38 | 6 | df-le2 131 | . . . . . . . . . 10 |
39 | 38 | lor 70 | . . . . . . . . 9 |
40 | 39 | lor 70 | . . . . . . . 8 |
41 | 11 | df-le2 131 | . . . . . . . 8 |
42 | 37, 40, 41 | 3tr 65 | . . . . . . 7 |
43 | 34, 42 | ax-r2 36 | . . . . . 6 |
44 | 31, 33, 43 | 3tr 65 | . . . . 5 |
45 | 24, 30, 44 | 3tr 65 | . . . 4 |
46 | 17, 20, 45 | 3tr 65 | . . 3 |
47 | 14, 15, 46 | 3tr2 64 | . 2 |
48 | df-i1 44 | . . 3 | |
49 | df-i3 46 | . . 3 | |
50 | 48, 49 | 2or 72 | . 2 |
51 | df-i0 43 | . 2 | |
52 | 47, 50, 51 | 3tr1 63 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 wt 8 wi0 11 wi1 12 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-i0 43 df-i1 44 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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