Proof of Theorem trlval4
Step | Hyp | Ref
| Expression |
1 | | simp1 1061 |
. 2
|
2 | | simp21 1094 |
. 2
|
3 | | simp22 1095 |
. 2
|
4 | | simp23 1096 |
. 2
|
5 | | simp3r 1090 |
. . 3
|
6 | | simpl1l 1112 |
. . . . . . . 8
|
7 | | simp23l 1182 |
. . . . . . . . 9
|
8 | 7 | adantr 481 |
. . . . . . . 8
|
9 | | simpl1 1064 |
. . . . . . . . 9
|
10 | | simpl21 1139 |
. . . . . . . . 9
|
11 | | trlval3.l |
. . . . . . . . . 10
|
12 | | trlval3.a |
. . . . . . . . . 10
|
13 | | trlval3.h |
. . . . . . . . . 10
|
14 | | trlval3.t |
. . . . . . . . . 10
|
15 | 11, 12, 13, 14 | ltrnat 35426 |
. . . . . . . . 9
|
16 | 9, 10, 8, 15 | syl3anc 1326 |
. . . . . . . 8
|
17 | | trlval3.j |
. . . . . . . . 9
|
18 | 11, 17, 12 | hlatlej1 34661 |
. . . . . . . 8
|
19 | 6, 8, 16, 18 | syl3anc 1326 |
. . . . . . 7
|
20 | | simpl22 1140 |
. . . . . . . . 9
|
21 | | trlval3.r |
. . . . . . . . . 10
|
22 | 11, 17, 12, 13, 14, 21 | trljat1 35453 |
. . . . . . . . 9
|
23 | 9, 10, 20, 22 | syl3anc 1326 |
. . . . . . . 8
|
24 | | simpr 477 |
. . . . . . . 8
|
25 | 23, 24 | eqtrd 2656 |
. . . . . . 7
|
26 | 19, 25 | breqtrrd 4681 |
. . . . . 6
|
27 | | simpl3r 1117 |
. . . . . . . . 9
|
28 | | simpll1 1100 |
. . . . . . . . . . . . 13
|
29 | 20 | adantr 481 |
. . . . . . . . . . . . 13
|
30 | 10 | adantr 481 |
. . . . . . . . . . . . 13
|
31 | | simpr 477 |
. . . . . . . . . . . . 13
|
32 | | eqid 2622 |
. . . . . . . . . . . . . 14
|
33 | 11, 32, 12, 13, 14, 21 | trl0 35457 |
. . . . . . . . . . . . 13
|
34 | 28, 29, 30, 31, 33 | syl112anc 1330 |
. . . . . . . . . . . 12
|
35 | | hlatl 34647 |
. . . . . . . . . . . . . . 15
|
36 | 6, 35 | syl 17 |
. . . . . . . . . . . . . 14
|
37 | | simp22l 1180 |
. . . . . . . . . . . . . . . 16
|
38 | 37 | adantr 481 |
. . . . . . . . . . . . . . 15
|
39 | | eqid 2622 |
. . . . . . . . . . . . . . . 16
|
40 | 39, 17, 12 | hlatjcl 34653 |
. . . . . . . . . . . . . . 15
|
41 | 6, 38, 8, 40 | syl3anc 1326 |
. . . . . . . . . . . . . 14
|
42 | 39, 11, 32 | atl0le 34591 |
. . . . . . . . . . . . . 14
|
43 | 36, 41, 42 | syl2anc 693 |
. . . . . . . . . . . . 13
|
44 | 43 | adantr 481 |
. . . . . . . . . . . 12
|
45 | 34, 44 | eqbrtrd 4675 |
. . . . . . . . . . 11
|
46 | 45 | ex 450 |
. . . . . . . . . 10
|
47 | 46 | necon3bd 2808 |
. . . . . . . . 9
|
48 | 27, 47 | mpd 15 |
. . . . . . . 8
|
49 | 11, 12, 13, 14, 21 | trlat 35456 |
. . . . . . . 8
|
50 | 9, 20, 10, 48, 49 | syl112anc 1330 |
. . . . . . 7
|
51 | | simpl3l 1116 |
. . . . . . . 8
|
52 | 51 | necomd 2849 |
. . . . . . 7
|
53 | 11, 17, 12 | hlatexch1 34681 |
. . . . . . 7
|
54 | 6, 8, 50, 38, 52, 53 | syl131anc 1339 |
. . . . . 6
|
55 | 26, 54 | mpd 15 |
. . . . 5
|
56 | 55 | ex 450 |
. . . 4
|
57 | 56 | necon3bd 2808 |
. . 3
|
58 | 5, 57 | mpd 15 |
. 2
|
59 | | trlval3.m |
. . 3
|
60 | 11, 17, 59, 12, 13, 14, 21 | trlval3 35474 |
. 2
|
61 | 1, 2, 3, 4, 58, 60 | syl113anc 1338 |
1
|