Proof of Theorem dalem54
Step | Hyp | Ref
| Expression |
1 | | dalem.ph |
. . . 4
|
2 | 1 | dalemkehl 34909 |
. . 3
|
3 | 2 | 3ad2ant1 1082 |
. 2
|
4 | | dalem.l |
. . . 4
|
5 | | dalem.j |
. . . 4
|
6 | | dalem.a |
. . . 4
|
7 | | dalem.ps |
. . . 4
|
8 | | dalem54.m |
. . . 4
|
9 | | dalem54.o |
. . . 4
|
10 | | dalem54.y |
. . . 4
|
11 | | dalem54.z |
. . . 4
|
12 | | dalem54.g |
. . . 4
|
13 | 1, 4, 5, 6, 7, 8, 9, 10, 11, 12 | dalem23 34982 |
. . 3
|
14 | | dalem54.h |
. . . 4
|
15 | 1, 4, 5, 6, 7, 8, 9, 10, 11, 14 | dalem29 34987 |
. . 3
|
16 | | dalem54.i |
. . . 4
|
17 | 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16 | dalem41 34999 |
. . 3
|
18 | | eqid 2622 |
. . . 4
|
19 | 5, 6, 18 | llni2 34798 |
. . 3
|
20 | 3, 13, 15, 17, 19 | syl31anc 1329 |
. 2
|
21 | | dalem54.b1 |
. . 3
|
22 | 1, 4, 5, 6, 7, 8, 18, 9, 10, 11, 12, 14, 16, 21 | dalem53 35011 |
. 2
|
23 | 1 | dalemkelat 34910 |
. . . . . . 7
|
24 | 23 | 3ad2ant1 1082 |
. . . . . 6
|
25 | | eqid 2622 |
. . . . . . . . 9
|
26 | 25, 18 | llnbase 34795 |
. . . . . . . 8
|
27 | 20, 26 | syl 17 |
. . . . . . 7
|
28 | 1, 4, 5, 6, 7, 8, 9, 10, 11, 16 | dalem34 34992 |
. . . . . . . 8
|
29 | 25, 6 | atbase 34576 |
. . . . . . . 8
|
30 | 28, 29 | syl 17 |
. . . . . . 7
|
31 | 25, 5 | latjcl 17051 |
. . . . . . 7
|
32 | 24, 27, 30, 31 | syl3anc 1326 |
. . . . . 6
|
33 | 1, 9 | dalemyeb 34935 |
. . . . . . 7
|
34 | 33 | 3ad2ant1 1082 |
. . . . . 6
|
35 | 25, 4, 8 | latmle2 17077 |
. . . . . 6
|
36 | 24, 32, 34, 35 | syl3anc 1326 |
. . . . 5
|
37 | 21, 36 | syl5eqbr 4688 |
. . . 4
|
38 | 1, 4, 5, 6, 7, 8, 9, 10, 11, 12 | dalem24 34983 |
. . . . 5
|
39 | 25, 6 | atbase 34576 |
. . . . . . . 8
|
40 | 13, 39 | syl 17 |
. . . . . . 7
|
41 | 25, 6 | atbase 34576 |
. . . . . . . 8
|
42 | 15, 41 | syl 17 |
. . . . . . 7
|
43 | 25, 4, 5 | latjle12 17062 |
. . . . . . 7
|
44 | 24, 40, 42, 34, 43 | syl13anc 1328 |
. . . . . 6
|
45 | | simpl 473 |
. . . . . 6
|
46 | 44, 45 | syl6bir 244 |
. . . . 5
|
47 | 38, 46 | mtod 189 |
. . . 4
|
48 | | nbrne2 4673 |
. . . 4
|
49 | 37, 47, 48 | syl2anc 693 |
. . 3
|
50 | 49 | necomd 2849 |
. 2
|
51 | | hlatl 34647 |
. . . 4
|
52 | 3, 51 | syl 17 |
. . 3
|
53 | 25, 18 | llnbase 34795 |
. . . . 5
|
54 | 22, 53 | syl 17 |
. . . 4
|
55 | 25, 8 | latmcl 17052 |
. . . 4
|
56 | 24, 27, 54, 55 | syl3anc 1326 |
. . 3
|
57 | 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16 | dalem52 35010 |
. . 3
|
58 | 1, 5, 6 | dalempjqeb 34931 |
. . . . . 6
|
59 | 58 | 3ad2ant1 1082 |
. . . . 5
|
60 | 25, 4, 8 | latmle1 17076 |
. . . . 5
|
61 | 24, 27, 59, 60 | syl3anc 1326 |
. . . 4
|
62 | 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16 | dalem51 35009 |
. . . . . 6
|
63 | 62 | simpld 475 |
. . . . 5
|
64 | 25, 6 | atbase 34576 |
. . . . . . . 8
|
65 | 64 | anim2i 593 |
. . . . . . 7
|
66 | 65 | 3anim1i 1248 |
. . . . . 6
|
67 | | biid 251 |
. . . . . . 7
|
68 | | eqid 2622 |
. . . . . . 7
|
69 | | eqid 2622 |
. . . . . . 7
|
70 | 67, 4, 5, 6, 8, 9, 68, 10, 21, 69 | dalem10 34959 |
. . . . . 6
|
71 | 66, 70 | syl3an1 1359 |
. . . . 5
|
72 | 63, 71 | syl 17 |
. . . 4
|
73 | 25, 8 | latmcl 17052 |
. . . . . 6
|
74 | 24, 27, 59, 73 | syl3anc 1326 |
. . . . 5
|
75 | 25, 4, 8 | latlem12 17078 |
. . . . 5
|
76 | 24, 74, 27, 54, 75 | syl13anc 1328 |
. . . 4
|
77 | 61, 72, 76 | mpbi2and 956 |
. . 3
|
78 | | eqid 2622 |
. . . 4
|
79 | 25, 4, 78, 6 | atlen0 34597 |
. . 3
|
80 | 52, 56, 57, 77, 79 | syl31anc 1329 |
. 2
|
81 | 8, 78, 6, 18 | 2llnmat 34810 |
. 2
|
82 | 3, 20, 22, 50, 80, 81 | syl32anc 1334 |
1
|