Proof of Theorem cdlemk52
Step | Hyp | Ref
| Expression |
1 | | cdlemk5.b |
. . . 4
|
2 | | cdlemk5.l |
. . . 4
|
3 | | simp11l 1172 |
. . . . 5
|
4 | | hllat 34650 |
. . . . 5
|
5 | 3, 4 | syl 17 |
. . . 4
|
6 | | simp11 1091 |
. . . . . 6
|
7 | | simp12 1092 |
. . . . . . . 8
|
8 | | simp13 1093 |
. . . . . . . 8
|
9 | | simp21 1094 |
. . . . . . . 8
|
10 | | simp22 1095 |
. . . . . . . 8
|
11 | | simp23 1096 |
. . . . . . . 8
|
12 | | cdlemk5.j |
. . . . . . . . 9
|
13 | | cdlemk5.m |
. . . . . . . . 9
|
14 | | cdlemk5.a |
. . . . . . . . 9
|
15 | | cdlemk5.h |
. . . . . . . . 9
|
16 | | cdlemk5.t |
. . . . . . . . 9
|
17 | | cdlemk5.r |
. . . . . . . . 9
|
18 | | cdlemk5.z |
. . . . . . . . 9
|
19 | | cdlemk5.y |
. . . . . . . . 9
|
20 | | cdlemk5.x |
. . . . . . . . 9
|
21 | 1, 2, 12, 13, 14, 15, 16, 17, 18, 19, 20 | cdlemk35s 36225 |
. . . . . . . 8
|
22 | 6, 7, 8, 9, 10, 11, 21 | syl132anc 1344 |
. . . . . . 7
|
23 | | simp31 1097 |
. . . . . . . . 9
|
24 | | simp32 1098 |
. . . . . . . . 9
|
25 | 23, 24 | jca 554 |
. . . . . . . 8
|
26 | 1, 2, 12, 13, 14, 15, 16, 17, 18, 19, 20 | cdlemk35s 36225 |
. . . . . . . 8
|
27 | 6, 7, 25, 9, 10, 11, 26 | syl132anc 1344 |
. . . . . . 7
|
28 | 15, 16 | ltrnco 36007 |
. . . . . . 7
|
29 | 6, 22, 27, 28 | syl3anc 1326 |
. . . . . 6
|
30 | | simp22l 1180 |
. . . . . 6
|
31 | 2, 14, 15, 16 | ltrnat 35426 |
. . . . . 6
|
32 | 6, 29, 30, 31 | syl3anc 1326 |
. . . . 5
|
33 | 1, 14 | atbase 34576 |
. . . . 5
|
34 | 32, 33 | syl 17 |
. . . 4
|
35 | 2, 14, 15, 16 | ltrnat 35426 |
. . . . . . . 8
|
36 | 6, 22, 30, 35 | syl3anc 1326 |
. . . . . . 7
|
37 | 1, 14 | atbase 34576 |
. . . . . . 7
|
38 | 36, 37 | syl 17 |
. . . . . 6
|
39 | 1, 15, 16, 17 | trlcl 35451 |
. . . . . . 7
|
40 | 6, 27, 39 | syl2anc 693 |
. . . . . 6
|
41 | 1, 12 | latjcl 17051 |
. . . . . 6
|
42 | 5, 38, 40, 41 | syl3anc 1326 |
. . . . 5
|
43 | 2, 14, 15, 16 | ltrnat 35426 |
. . . . . . . 8
|
44 | 6, 27, 30, 43 | syl3anc 1326 |
. . . . . . 7
|
45 | 1, 14 | atbase 34576 |
. . . . . . 7
|
46 | 44, 45 | syl 17 |
. . . . . 6
|
47 | 1, 15, 16, 17 | trlcl 35451 |
. . . . . . 7
|
48 | 6, 22, 47 | syl2anc 693 |
. . . . . 6
|
49 | 1, 12 | latjcl 17051 |
. . . . . 6
|
50 | 5, 46, 48, 49 | syl3anc 1326 |
. . . . 5
|
51 | 1, 13 | latmcl 17052 |
. . . . 5
|
52 | 5, 42, 50, 51 | syl3anc 1326 |
. . . 4
|
53 | | simp11r 1173 |
. . . . . . 7
|
54 | 1, 14, 15, 16, 17 | trlnidat 35460 |
. . . . . . 7
|
55 | 3, 53, 23, 24, 54 | syl211anc 1332 |
. . . . . 6
|
56 | 1, 12, 14 | hlatjcl 34653 |
. . . . . 6
|
57 | 3, 36, 55, 56 | syl3anc 1326 |
. . . . 5
|
58 | | simp13l 1176 |
. . . . . . 7
|
59 | | simp13r 1177 |
. . . . . . 7
|
60 | 1, 14, 15, 16, 17 | trlnidat 35460 |
. . . . . . 7
|
61 | 3, 53, 58, 59, 60 | syl211anc 1332 |
. . . . . 6
|
62 | 1, 12, 14 | hlatjcl 34653 |
. . . . . 6
|
63 | 3, 44, 61, 62 | syl3anc 1326 |
. . . . 5
|
64 | 1, 13 | latmcl 17052 |
. . . . 5
|
65 | 5, 57, 63, 64 | syl3anc 1326 |
. . . 4
|
66 | 1, 2, 12, 13, 14, 15, 16, 17, 18, 19, 20 | cdlemk50 36240 |
. . . . 5
|
67 | 25, 66 | syld3an3 1371 |
. . . 4
|
68 | 1, 2, 12, 13, 14, 15, 16, 17, 18, 19, 20 | cdlemk51 36241 |
. . . . 5
|
69 | 25, 68 | syld3an3 1371 |
. . . 4
|
70 | 1, 2, 5, 34, 52, 65, 67, 69 | lattrd 17058 |
. . 3
|
71 | 1, 2, 12, 13, 14, 15, 16, 17, 18, 19, 20 | cdlemk47 36237 |
. . 3
|
72 | 70, 71 | breqtrrd 4681 |
. 2
|
73 | | hlatl 34647 |
. . . 4
|
74 | 3, 73 | syl 17 |
. . 3
|
75 | 15, 16 | ltrnco 36007 |
. . . . . . 7
|
76 | 6, 58, 23, 75 | syl3anc 1326 |
. . . . . 6
|
77 | 58, 23 | jca 554 |
. . . . . . 7
|
78 | | simp33 1099 |
. . . . . . 7
|
79 | 1, 15, 16, 17 | trlconid 36013 |
. . . . . . 7
|
80 | 6, 77, 78, 79 | syl3anc 1326 |
. . . . . 6
|
81 | 76, 80 | jca 554 |
. . . . 5
|
82 | 1, 2, 12, 13, 14, 15, 16, 17, 18, 19, 20 | cdlemk35s 36225 |
. . . . 5
|
83 | 6, 7, 81, 9, 10, 11, 82 | syl132anc 1344 |
. . . 4
|
84 | 2, 14, 15, 16 | ltrnat 35426 |
. . . 4
|
85 | 6, 83, 30, 84 | syl3anc 1326 |
. . 3
|
86 | 2, 14 | atcmp 34598 |
. . 3
|
87 | 74, 32, 85, 86 | syl3anc 1326 |
. 2
|
88 | 72, 87 | mpbid 222 |
1
|