Proof of Theorem cdleme20d
Step | Hyp | Ref
| Expression |
1 | | simp11l 1172 |
. . . 4
|
2 | | hlol 34648 |
. . . 4
|
3 | 1, 2 | syl 17 |
. . 3
|
4 | | hllat 34650 |
. . . . 5
|
5 | 1, 4 | syl 17 |
. . . 4
|
6 | | simp11r 1173 |
. . . . 5
|
7 | | simp12l 1174 |
. . . . 5
|
8 | | simp13l 1176 |
. . . . 5
|
9 | | simp21l 1178 |
. . . . 5
|
10 | | cdleme19.l |
. . . . . 6
|
11 | | cdleme19.j |
. . . . . 6
|
12 | | cdleme19.m |
. . . . . 6
|
13 | | cdleme19.a |
. . . . . 6
|
14 | | cdleme19.h |
. . . . . 6
|
15 | | cdleme19.u |
. . . . . 6
|
16 | | cdleme19.f |
. . . . . 6
|
17 | | eqid 2622 |
. . . . . 6
|
18 | 10, 11, 12, 13, 14, 15, 16, 17 | cdleme1b 35513 |
. . . . 5
|
19 | 1, 6, 7, 8, 9, 18 | syl23anc 1333 |
. . . 4
|
20 | | simp22l 1180 |
. . . . 5
|
21 | | cdleme19.g |
. . . . . 6
|
22 | 10, 11, 12, 13, 14, 15, 21, 17 | cdleme1b 35513 |
. . . . 5
|
23 | 1, 6, 7, 8, 20, 22 | syl23anc 1333 |
. . . 4
|
24 | 17, 11 | latjcl 17051 |
. . . 4
|
25 | 5, 19, 23, 24 | syl3anc 1326 |
. . 3
|
26 | 17, 14 | lhpbase 35284 |
. . . 4
|
27 | 6, 26 | syl 17 |
. . 3
|
28 | | simp23l 1182 |
. . . . 5
|
29 | 17, 11, 13 | hlatjcl 34653 |
. . . . 5
|
30 | 1, 28, 9, 29 | syl3anc 1326 |
. . . 4
|
31 | 17, 13 | atbase 34576 |
. . . . 5
|
32 | 20, 31 | syl 17 |
. . . 4
|
33 | 17, 11 | latjcl 17051 |
. . . 4
|
34 | 5, 30, 32, 33 | syl3anc 1326 |
. . 3
|
35 | 17, 12 | latmassOLD 34516 |
. . 3
|
36 | 3, 25, 27, 34, 35 | syl13anc 1328 |
. 2
|
37 | 10, 11, 13 | hlatlej2 34662 |
. . . . . . . 8
|
38 | 1, 28, 9, 37 | syl3anc 1326 |
. . . . . . 7
|
39 | 17, 13 | atbase 34576 |
. . . . . . . . 9
|
40 | 9, 39 | syl 17 |
. . . . . . . 8
|
41 | 17, 10, 11 | latjlej1 17065 |
. . . . . . . 8
|
42 | 5, 40, 30, 32, 41 | syl13anc 1328 |
. . . . . . 7
|
43 | 38, 42 | mpd 15 |
. . . . . 6
|
44 | 17, 11, 13 | hlatjcl 34653 |
. . . . . . . 8
|
45 | 1, 9, 20, 44 | syl3anc 1326 |
. . . . . . 7
|
46 | 17, 10, 12 | latleeqm1 17079 |
. . . . . . 7
|
47 | 5, 45, 34, 46 | syl3anc 1326 |
. . . . . 6
|
48 | 43, 47 | mpbid 222 |
. . . . 5
|
49 | 48 | oveq1d 6665 |
. . . 4
|
50 | | cdleme20.v |
. . . 4
|
51 | 49, 50 | syl6reqr 2675 |
. . 3
|
52 | 17, 12 | latm32 34518 |
. . . . 5
|
53 | 3, 45, 34, 27, 52 | syl13anc 1328 |
. . . 4
|
54 | | simp1 1061 |
. . . . . 6
|
55 | | simp21 1094 |
. . . . . 6
|
56 | | simp22 1095 |
. . . . . 6
|
57 | | simp31 1097 |
. . . . . 6
|
58 | | simp32l 1186 |
. . . . . 6
|
59 | | simp32r 1187 |
. . . . . 6
|
60 | 10, 11, 12, 13, 14, 15, 16, 21 | cdleme16 35572 |
. . . . . 6
|
61 | 54, 55, 56, 57, 58, 59, 60 | syl132anc 1344 |
. . . . 5
|
62 | 61 | oveq1d 6665 |
. . . 4
|
63 | 53, 62 | eqtrd 2656 |
. . 3
|
64 | 51, 63 | eqtrd 2656 |
. 2
|
65 | | simp23 1096 |
. . . . 5
|
66 | | simp33 1099 |
. . . . 5
|
67 | | cdleme19.d |
. . . . . 6
|
68 | | cdleme19.y |
. . . . . 6
|
69 | 10, 11, 12, 13, 14, 15, 16, 21, 67, 68, 50 | cdleme20c 35599 |
. . . . 5
|
70 | 1, 6, 65, 55, 20, 58, 66, 69 | syl232anc 1353 |
. . . 4
|
71 | 17, 12 | latmcom 17075 |
. . . . 5
|
72 | 5, 34, 27, 71 | syl3anc 1326 |
. . . 4
|
73 | 70, 72 | eqtrd 2656 |
. . 3
|
74 | 73 | oveq2d 6666 |
. 2
|
75 | 36, 64, 74 | 3eqtr4rd 2667 |
1
|