Proof of Theorem cdleme7e
Step | Hyp | Ref
| Expression |
1 | | simp11l 1172 |
. . . 4
|
2 | | hllat 34650 |
. . . . . 6
|
3 | 1, 2 | syl 17 |
. . . . 5
|
4 | | simp2ll 1128 |
. . . . . 6
|
5 | | eqid 2622 |
. . . . . . 7
|
6 | | cdleme4.a |
. . . . . . 7
|
7 | 5, 6 | atbase 34576 |
. . . . . 6
|
8 | 4, 7 | syl 17 |
. . . . 5
|
9 | | hlop 34649 |
. . . . . 6
|
10 | | eqid 2622 |
. . . . . . 7
|
11 | 5, 10 | op0cl 34471 |
. . . . . 6
|
12 | 1, 9, 11 | 3syl 18 |
. . . . 5
|
13 | | cdleme4.j |
. . . . . 6
|
14 | 5, 13 | latjcl 17051 |
. . . . 5
|
15 | 3, 8, 12, 14 | syl3anc 1326 |
. . . 4
|
16 | | cdleme4.g |
. . . . . 6
|
17 | | simp12l 1174 |
. . . . . . . 8
|
18 | | simp13l 1176 |
. . . . . . . 8
|
19 | 5, 13, 6 | hlatjcl 34653 |
. . . . . . . 8
|
20 | 1, 17, 18, 19 | syl3anc 1326 |
. . . . . . 7
|
21 | | simp11 1091 |
. . . . . . . . 9
|
22 | | simp2rl 1130 |
. . . . . . . . 9
|
23 | | cdleme4.l |
. . . . . . . . . 10
|
24 | | cdleme4.m |
. . . . . . . . . 10
|
25 | | cdleme4.h |
. . . . . . . . . 10
|
26 | | cdleme4.u |
. . . . . . . . . 10
|
27 | | cdleme4.f |
. . . . . . . . . 10
|
28 | 23, 13, 24, 6, 25, 26, 27, 5 | cdleme1b 35513 |
. . . . . . . . 9
|
29 | 21, 17, 18, 22, 28 | syl13anc 1328 |
. . . . . . . 8
|
30 | 5, 13, 6 | hlatjcl 34653 |
. . . . . . . . . 10
|
31 | 1, 4, 22, 30 | syl3anc 1326 |
. . . . . . . . 9
|
32 | | simp11r 1173 |
. . . . . . . . . 10
|
33 | 5, 25 | lhpbase 35284 |
. . . . . . . . . 10
|
34 | 32, 33 | syl 17 |
. . . . . . . . 9
|
35 | 5, 24 | latmcl 17052 |
. . . . . . . . 9
|
36 | 3, 31, 34, 35 | syl3anc 1326 |
. . . . . . . 8
|
37 | 5, 13 | latjcl 17051 |
. . . . . . . 8
|
38 | 3, 29, 36, 37 | syl3anc 1326 |
. . . . . . 7
|
39 | 5, 24 | latmcl 17052 |
. . . . . . 7
|
40 | 3, 20, 38, 39 | syl3anc 1326 |
. . . . . 6
|
41 | 16, 40 | syl5eqel 2705 |
. . . . 5
|
42 | 5, 13 | latjcl 17051 |
. . . . 5
|
43 | 3, 8, 41, 42 | syl3anc 1326 |
. . . 4
|
44 | 5, 23, 24 | latmle2 17077 |
. . . . . . . . 9
|
45 | 3, 20, 34, 44 | syl3anc 1326 |
. . . . . . . 8
|
46 | 26, 45 | syl5eqbr 4688 |
. . . . . . 7
|
47 | | simp2lr 1129 |
. . . . . . 7
|
48 | | nbrne2 4673 |
. . . . . . . 8
|
49 | 48 | necomd 2849 |
. . . . . . 7
|
50 | 46, 47, 49 | syl2anc 693 |
. . . . . 6
|
51 | | simp12 1092 |
. . . . . . . 8
|
52 | | simp31 1097 |
. . . . . . . 8
|
53 | 23, 13, 24, 6, 25, 26 | lhpat2 35331 |
. . . . . . . 8
|
54 | 21, 51, 18, 52, 53 | syl112anc 1330 |
. . . . . . 7
|
55 | | eqid 2622 |
. . . . . . . 8
|
56 | 13, 55, 6 | atcvr1 34703 |
. . . . . . 7
|
57 | 1, 4, 54, 56 | syl3anc 1326 |
. . . . . 6
|
58 | 50, 57 | mpbid 222 |
. . . . 5
|
59 | | hlol 34648 |
. . . . . . 7
|
60 | 1, 59 | syl 17 |
. . . . . 6
|
61 | 5, 13, 10 | olj01 34512 |
. . . . . 6
|
62 | 60, 8, 61 | syl2anc 693 |
. . . . 5
|
63 | | simp2l 1087 |
. . . . . . 7
|
64 | | simp2r 1088 |
. . . . . . 7
|
65 | | simp32 1098 |
. . . . . . 7
|
66 | 23, 13, 24, 6, 25, 26, 27, 16 | cdleme5 35527 |
. . . . . . 7
|
67 | 21, 17, 18, 63, 64, 65, 66 | syl132anc 1344 |
. . . . . 6
|
68 | 23, 13, 24, 6, 25, 26 | cdleme4 35525 |
. . . . . . 7
|
69 | 21, 17, 18, 63, 65, 68 | syl131anc 1339 |
. . . . . 6
|
70 | 67, 69 | eqtrd 2656 |
. . . . 5
|
71 | 58, 62, 70 | 3brtr4d 4685 |
. . . 4
|
72 | 5, 55 | cvrne 34568 |
. . . 4
|
73 | 1, 15, 43, 71, 72 | syl31anc 1329 |
. . 3
|
74 | | oveq2 6658 |
. . . 4
|
75 | 74 | necon3i 2826 |
. . 3
|
76 | 73, 75 | syl 17 |
. 2
|
77 | 76 | necomd 2849 |
1
|