Proof of Theorem cdleme11
Step | Hyp | Ref
| Expression |
1 | | simp11l 1172 |
. . . . . . . . 9
|
2 | | hllat 34650 |
. . . . . . . . 9
|
3 | 1, 2 | syl 17 |
. . . . . . . 8
|
4 | | simp11 1091 |
. . . . . . . . 9
|
5 | | simp12l 1174 |
. . . . . . . . 9
|
6 | | simp13l 1176 |
. . . . . . . . 9
|
7 | | cdleme12.l |
. . . . . . . . . 10
|
8 | | cdleme12.j |
. . . . . . . . . 10
|
9 | | cdleme12.m |
. . . . . . . . . 10
|
10 | | cdleme12.a |
. . . . . . . . . 10
|
11 | | cdleme12.h |
. . . . . . . . . 10
|
12 | | cdleme12.u |
. . . . . . . . . 10
|
13 | | eqid 2622 |
. . . . . . . . . 10
|
14 | 7, 8, 9, 10, 11, 12, 13 | cdleme0aa 35497 |
. . . . . . . . 9
|
15 | 4, 5, 6, 14 | syl3anc 1326 |
. . . . . . . 8
|
16 | 13, 8 | latjidm 17074 |
. . . . . . . 8
|
17 | 3, 15, 16 | syl2anc 693 |
. . . . . . 7
|
18 | 17 | oveq2d 6666 |
. . . . . 6
|
19 | | simp33 1099 |
. . . . . . 7
|
20 | | simp21l 1178 |
. . . . . . . . . 10
|
21 | 13, 10 | atbase 34576 |
. . . . . . . . . 10
|
22 | 20, 21 | syl 17 |
. . . . . . . . 9
|
23 | | simp22l 1180 |
. . . . . . . . . 10
|
24 | 13, 10 | atbase 34576 |
. . . . . . . . . 10
|
25 | 23, 24 | syl 17 |
. . . . . . . . 9
|
26 | 13, 8 | latjcl 17051 |
. . . . . . . . 9
|
27 | 3, 22, 25, 26 | syl3anc 1326 |
. . . . . . . 8
|
28 | 13, 7, 8 | latleeqj2 17064 |
. . . . . . . 8
|
29 | 3, 15, 27, 28 | syl3anc 1326 |
. . . . . . 7
|
30 | 19, 29 | mpbid 222 |
. . . . . 6
|
31 | 18, 30 | eqtr2d 2657 |
. . . . 5
|
32 | | simp21 1094 |
. . . . . . . 8
|
33 | | cdleme12.f |
. . . . . . . . 9
|
34 | 7, 8, 9, 10, 11, 12, 33 | cdleme1 35514 |
. . . . . . . 8
|
35 | 4, 5, 6, 32, 34 | syl13anc 1328 |
. . . . . . 7
|
36 | | simp22 1095 |
. . . . . . . 8
|
37 | | cdleme12.g |
. . . . . . . . 9
|
38 | 7, 8, 9, 10, 11, 12, 37 | cdleme1 35514 |
. . . . . . . 8
|
39 | 4, 5, 6, 36, 38 | syl13anc 1328 |
. . . . . . 7
|
40 | 35, 39 | oveq12d 6668 |
. . . . . 6
|
41 | 13, 8 | latj4 17101 |
. . . . . . 7
|
42 | 3, 22, 25, 15, 15, 41 | syl122anc 1335 |
. . . . . 6
|
43 | 40, 42 | eqtr4d 2659 |
. . . . 5
|
44 | 31, 43 | eqtr4d 2659 |
. . . 4
|
45 | 7, 8, 9, 10, 11, 12, 33, 13 | cdleme1b 35513 |
. . . . . 6
|
46 | 4, 5, 6, 20, 45 | syl13anc 1328 |
. . . . 5
|
47 | 7, 8, 9, 10, 11, 12, 37, 13 | cdleme1b 35513 |
. . . . . 6
|
48 | 4, 5, 6, 23, 47 | syl13anc 1328 |
. . . . 5
|
49 | 13, 8 | latj4 17101 |
. . . . 5
|
50 | 3, 22, 46, 25, 48, 49 | syl122anc 1335 |
. . . 4
|
51 | 44, 50 | eqtr2d 2657 |
. . 3
|
52 | 13, 8 | latjcl 17051 |
. . . . 5
|
53 | 3, 46, 48, 52 | syl3anc 1326 |
. . . 4
|
54 | 13, 7, 8 | latleeqj2 17064 |
. . . 4
|
55 | 3, 53, 27, 54 | syl3anc 1326 |
. . 3
|
56 | 51, 55 | mpbird 247 |
. 2
|
57 | | simp12 1092 |
. . . 4
|
58 | | simp13 1093 |
. . . 4
|
59 | | simp23l 1182 |
. . . 4
|
60 | | simp31 1097 |
. . . 4
|
61 | 7, 8, 9, 10, 11, 12, 33 | cdleme3fa 35523 |
. . . 4
|
62 | 4, 57, 58, 32, 59, 60, 61 | syl132anc 1344 |
. . 3
|
63 | | simp32 1098 |
. . . 4
|
64 | 7, 8, 9, 10, 11, 12, 37 | cdleme3fa 35523 |
. . . 4
|
65 | 4, 57, 58, 36, 59, 63, 64 | syl132anc 1344 |
. . 3
|
66 | 7, 8, 9, 10, 11, 12, 33, 37 | cdleme11l 35556 |
. . 3
|
67 | 7, 8, 10 | ps-1 34763 |
. . 3
|
68 | 1, 62, 65, 66, 20, 23, 67 | syl132anc 1344 |
. 2
|
69 | 56, 68 | mpbid 222 |
1
|