Proof of Theorem trljco
Step | Hyp | Ref
| Expression |
1 | | coeq1 5279 |
. . . . 5
|
2 | | eqid 2622 |
. . . . . . . 8
|
3 | | trljco.h |
. . . . . . . 8
|
4 | | trljco.t |
. . . . . . . 8
|
5 | 2, 3, 4 | ltrn1o 35410 |
. . . . . . 7
|
6 | 5 | 3adant2 1080 |
. . . . . 6
|
7 | | f1of 6137 |
. . . . . 6
|
8 | | fcoi2 6079 |
. . . . . 6
|
9 | 6, 7, 8 | 3syl 18 |
. . . . 5
|
10 | 1, 9 | sylan9eqr 2678 |
. . . 4
|
11 | 10 | fveq2d 6195 |
. . 3
|
12 | 11 | oveq2d 6666 |
. 2
|
13 | | simp1l 1085 |
. . . . . . 7
|
14 | | hllat 34650 |
. . . . . . 7
|
15 | 13, 14 | syl 17 |
. . . . . 6
|
16 | | trljco.r |
. . . . . . . 8
|
17 | 2, 3, 4, 16 | trlcl 35451 |
. . . . . . 7
|
18 | 17 | 3adant3 1081 |
. . . . . 6
|
19 | | trljco.j |
. . . . . . 7
|
20 | 2, 19 | latjidm 17074 |
. . . . . 6
|
21 | 15, 18, 20 | syl2anc 693 |
. . . . 5
|
22 | | hlol 34648 |
. . . . . . 7
|
23 | 13, 22 | syl 17 |
. . . . . 6
|
24 | | eqid 2622 |
. . . . . . 7
|
25 | 2, 19, 24 | olj01 34512 |
. . . . . 6
|
26 | 23, 18, 25 | syl2anc 693 |
. . . . 5
|
27 | 21, 26 | eqtr4d 2659 |
. . . 4
|
28 | 27 | adantr 481 |
. . 3
|
29 | | coeq2 5280 |
. . . . . 6
|
30 | 2, 3, 4 | ltrn1o 35410 |
. . . . . . . 8
|
31 | 30 | 3adant3 1081 |
. . . . . . 7
|
32 | | f1of 6137 |
. . . . . . 7
|
33 | | fcoi1 6078 |
. . . . . . 7
|
34 | 31, 32, 33 | 3syl 18 |
. . . . . 6
|
35 | 29, 34 | sylan9eqr 2678 |
. . . . 5
|
36 | 35 | fveq2d 6195 |
. . . 4
|
37 | 36 | oveq2d 6666 |
. . 3
|
38 | 2, 24, 3, 4, 16 | trlid0b 35465 |
. . . . . 6
|
39 | 38 | 3adant2 1080 |
. . . . 5
|
40 | 39 | biimpa 501 |
. . . 4
|
41 | 40 | oveq2d 6666 |
. . 3
|
42 | 28, 37, 41 | 3eqtr4d 2666 |
. 2
|
43 | | eqid 2622 |
. . 3
|
44 | 15 | adantr 481 |
. . 3
|
45 | | simp1 1061 |
. . . . . 6
|
46 | 3, 4 | ltrnco 36007 |
. . . . . 6
|
47 | 2, 3, 4, 16 | trlcl 35451 |
. . . . . 6
|
48 | 45, 46, 47 | syl2anc 693 |
. . . . 5
|
49 | 2, 19 | latjcl 17051 |
. . . . 5
|
50 | 15, 18, 48, 49 | syl3anc 1326 |
. . . 4
|
51 | 50 | adantr 481 |
. . 3
|
52 | 2, 3, 4, 16 | trlcl 35451 |
. . . . . 6
|
53 | 52 | 3adant2 1080 |
. . . . 5
|
54 | 2, 19 | latjcl 17051 |
. . . . 5
|
55 | 15, 18, 53, 54 | syl3anc 1326 |
. . . 4
|
56 | 55 | adantr 481 |
. . 3
|
57 | 2, 43, 19 | latlej1 17060 |
. . . . . 6
|
58 | 15, 18, 53, 57 | syl3anc 1326 |
. . . . 5
|
59 | 43, 19, 3, 4, 16 | trlco 36015 |
. . . . 5
|
60 | 2, 43, 19 | latjle12 17062 |
. . . . . 6
|
61 | 15, 18, 48, 55, 60 | syl13anc 1328 |
. . . . 5
|
62 | 58, 59, 61 | mpbi2and 956 |
. . . 4
|
63 | 62 | adantr 481 |
. . 3
|
64 | | simpr 477 |
. . . . 5
|
65 | 64 | oveq2d 6666 |
. . . 4
|
66 | 2, 43, 19 | latlej1 17060 |
. . . . . . 7
|
67 | 15, 18, 48, 66 | syl3anc 1326 |
. . . . . 6
|
68 | 21, 67 | eqbrtrd 4675 |
. . . . 5
|
69 | 68 | adantr 481 |
. . . 4
|
70 | 65, 69 | eqbrtrrd 4677 |
. . 3
|
71 | 2, 43, 44, 51, 56, 63, 70 | latasymd 17057 |
. 2
|
72 | 62 | adantr 481 |
. . 3
|
73 | | simpl1l 1112 |
. . . 4
|
74 | | simpl1 1064 |
. . . . 5
|
75 | | simpl2 1065 |
. . . . 5
|
76 | | simpr1 1067 |
. . . . 5
|
77 | | eqid 2622 |
. . . . . 6
|
78 | 2, 77, 3, 4, 16 | trlnidat 35460 |
. . . . 5
|
79 | 74, 75, 76, 78 | syl3anc 1326 |
. . . 4
|
80 | | simpl3 1066 |
. . . . . 6
|
81 | 75, 80 | jca 554 |
. . . . 5
|
82 | | simpr3 1069 |
. . . . 5
|
83 | 77, 3, 4, 16 | trlcoat 36011 |
. . . . 5
|
84 | 74, 81, 82, 83 | syl3anc 1326 |
. . . 4
|
85 | | simpr2 1068 |
. . . . 5
|
86 | 2, 3, 4, 16 | trlcone 36016 |
. . . . 5
|
87 | 74, 81, 82, 85, 86 | syl112anc 1330 |
. . . 4
|
88 | 2, 77, 3, 4, 16 | trlnidat 35460 |
. . . . 5
|
89 | 74, 80, 85, 88 | syl3anc 1326 |
. . . 4
|
90 | 43, 19, 77 | ps-1 34763 |
. . . 4
|
91 | 73, 79, 84, 87, 79, 89, 90 | syl132anc 1344 |
. . 3
|
92 | 72, 91 | mpbid 222 |
. 2
|
93 | 12, 42, 71, 92 | pm2.61da3ne 2883 |
1
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