Proof of Theorem cdlema1N
Step | Hyp | Ref
| Expression |
1 | | cdlema1.b |
. 2
|
2 | | cdlema1.l |
. 2
|
3 | | simp11 1091 |
. . 3
|
4 | | hllat 34650 |
. . 3
|
5 | 3, 4 | syl 17 |
. 2
|
6 | | simp12 1092 |
. . 3
|
7 | | simp23 1096 |
. . . 4
|
8 | | cdlema1.a |
. . . . 5
|
9 | 1, 8 | atbase 34576 |
. . . 4
|
10 | 7, 9 | syl 17 |
. . 3
|
11 | | cdlema1.j |
. . . 4
|
12 | 1, 11 | latjcl 17051 |
. . 3
|
13 | 5, 6, 10, 12 | syl3anc 1326 |
. 2
|
14 | | simp13 1093 |
. . 3
|
15 | 1, 11 | latjcl 17051 |
. . 3
|
16 | 5, 6, 14, 15 | syl3anc 1326 |
. 2
|
17 | 1, 2, 11 | latlej1 17060 |
. . . 4
|
18 | 5, 6, 14, 17 | syl3anc 1326 |
. . 3
|
19 | | simp21 1094 |
. . . . . 6
|
20 | 1, 8 | atbase 34576 |
. . . . . 6
|
21 | 19, 20 | syl 17 |
. . . . 5
|
22 | | simp22 1095 |
. . . . . 6
|
23 | 1, 8 | atbase 34576 |
. . . . . 6
|
24 | 22, 23 | syl 17 |
. . . . 5
|
25 | 1, 11 | latjcl 17051 |
. . . . 5
|
26 | 5, 21, 24, 25 | syl3anc 1326 |
. . . 4
|
27 | | simp31r 1185 |
. . . 4
|
28 | | simp32l 1186 |
. . . . 5
|
29 | | simp32r 1187 |
. . . . 5
|
30 | 1, 2, 11 | latjlej12 17067 |
. . . . . 6
|
31 | 5, 21, 6, 24, 14, 30 | syl122anc 1335 |
. . . . 5
|
32 | 28, 29, 31 | mp2and 715 |
. . . 4
|
33 | 1, 2, 5, 10, 26, 16, 27, 32 | lattrd 17058 |
. . 3
|
34 | 1, 2, 11 | latjle12 17062 |
. . . 4
|
35 | 5, 6, 10, 16, 34 | syl13anc 1328 |
. . 3
|
36 | 18, 33, 35 | mpbi2and 956 |
. 2
|
37 | 1, 2, 11 | latlej1 17060 |
. . . 4
|
38 | 5, 6, 10, 37 | syl3anc 1326 |
. . 3
|
39 | | simp331 1214 |
. . . . 5
|
40 | | simp332 1215 |
. . . . 5
|
41 | | simp333 1216 |
. . . . . 6
|
42 | | cdlema1.m |
. . . . . . . . . 10
|
43 | 1, 2, 42 | latmle1 17076 |
. . . . . . . . 9
|
44 | 5, 6, 14, 43 | syl3anc 1326 |
. . . . . . . 8
|
45 | | breq1 4656 |
. . . . . . . 8
|
46 | 44, 45 | syl5ibrcom 237 |
. . . . . . 7
|
47 | 46 | necon3bd 2808 |
. . . . . 6
|
48 | 41, 47 | mpd 15 |
. . . . 5
|
49 | 1, 2, 42 | latmle2 17077 |
. . . . . 6
|
50 | 5, 6, 14, 49 | syl3anc 1326 |
. . . . 5
|
51 | | cdlema1.n |
. . . . . 6
|
52 | | cdlema1.f |
. . . . . 6
|
53 | 1, 2, 11, 8, 51, 52 | lneq2at 35064 |
. . . . 5
|
54 | 3, 14, 39, 22, 40, 48, 29, 50, 53 | syl332anc 1357 |
. . . 4
|
55 | 1, 11 | latjcl 17051 |
. . . . . . 7
|
56 | 5, 21, 10, 55 | syl3anc 1326 |
. . . . . 6
|
57 | 7, 22, 19 | 3jca 1242 |
. . . . . . . 8
|
58 | | simp31l 1184 |
. . . . . . . 8
|
59 | 3, 57, 58 | 3jca 1242 |
. . . . . . 7
|
60 | 2, 11, 8 | hlatexch1 34681 |
. . . . . . 7
|
61 | 59, 27, 60 | sylc 65 |
. . . . . 6
|
62 | 21, 6, 10 | 3jca 1242 |
. . . . . . . 8
|
63 | 5, 62 | jca 554 |
. . . . . . 7
|
64 | 1, 2, 11 | latjlej1 17065 |
. . . . . . 7
|
65 | 63, 28, 64 | sylc 65 |
. . . . . 6
|
66 | 1, 2, 5, 24, 56, 13, 61, 65 | lattrd 17058 |
. . . . 5
|
67 | 1, 2, 11, 42 | latmlej11 17090 |
. . . . . 6
|
68 | 5, 6, 14, 10, 67 | syl13anc 1328 |
. . . . 5
|
69 | 1, 42 | latmcl 17052 |
. . . . . . 7
|
70 | 5, 6, 14, 69 | syl3anc 1326 |
. . . . . 6
|
71 | 1, 2, 11 | latjle12 17062 |
. . . . . 6
|
72 | 5, 24, 70, 13, 71 | syl13anc 1328 |
. . . . 5
|
73 | 66, 68, 72 | mpbi2and 956 |
. . . 4
|
74 | 54, 73 | eqbrtrd 4675 |
. . 3
|
75 | 1, 2, 11 | latjle12 17062 |
. . . 4
|
76 | 5, 6, 14, 13, 75 | syl13anc 1328 |
. . 3
|
77 | 38, 74, 76 | mpbi2and 956 |
. 2
|
78 | 1, 2, 5, 13, 16, 36, 77 | latasymd 17057 |
1
|