Step | Hyp | Ref
| Expression |
1 | | imasmnd.u |
. . . 4
s |
2 | | imasmnd.v |
. . . 4
|
3 | | imasmnd.f |
. . . 4
|
4 | | imasmnd2.r |
. . . 4
|
5 | 1, 2, 3, 4 | imasbas 16172 |
. . 3
|
6 | | eqidd 2623 |
. . 3
|
7 | | imasmnd.e |
. . . . 5
|
8 | | imasmnd.p |
. . . . 5
|
9 | | eqid 2622 |
. . . . 5
|
10 | | imasmnd2.1 |
. . . . . . 7
|
11 | 10 | 3expb 1266 |
. . . . . 6
|
12 | 11 | caovclg 6826 |
. . . . 5
|
13 | 3, 7, 1, 2, 4, 8, 9, 12 | imasaddf 16193 |
. . . 4
|
14 | | fovrn 6804 |
. . . 4
|
15 | 13, 14 | syl3an1 1359 |
. . 3
|
16 | | forn 6118 |
. . . . . . . . . 10
|
17 | 3, 16 | syl 17 |
. . . . . . . . 9
|
18 | 17 | eleq2d 2687 |
. . . . . . . 8
|
19 | 17 | eleq2d 2687 |
. . . . . . . 8
|
20 | 17 | eleq2d 2687 |
. . . . . . . 8
|
21 | 18, 19, 20 | 3anbi123d 1399 |
. . . . . . 7
|
22 | | fofn 6117 |
. . . . . . . . 9
|
23 | 3, 22 | syl 17 |
. . . . . . . 8
|
24 | | fvelrnb 6243 |
. . . . . . . . 9
|
25 | | fvelrnb 6243 |
. . . . . . . . 9
|
26 | | fvelrnb 6243 |
. . . . . . . . 9
|
27 | 24, 25, 26 | 3anbi123d 1399 |
. . . . . . . 8
|
28 | 23, 27 | syl 17 |
. . . . . . 7
|
29 | 21, 28 | bitr3d 270 |
. . . . . 6
|
30 | | 3reeanv 3108 |
. . . . . 6
|
31 | 29, 30 | syl6bbr 278 |
. . . . 5
|
32 | | imasmnd2.2 |
. . . . . . . . . . . 12
|
33 | | simpl 473 |
. . . . . . . . . . . . 13
|
34 | 10 | 3adant3r3 1276 |
. . . . . . . . . . . . 13
|
35 | | simpr3 1069 |
. . . . . . . . . . . . 13
|
36 | 3, 7, 1, 2, 4, 8, 9 | imasaddval 16192 |
. . . . . . . . . . . . 13
|
37 | 33, 34, 35, 36 | syl3anc 1326 |
. . . . . . . . . . . 12
|
38 | | simpr1 1067 |
. . . . . . . . . . . . 13
|
39 | 12 | caovclg 6826 |
. . . . . . . . . . . . . 14
|
40 | 39 | 3adantr1 1220 |
. . . . . . . . . . . . 13
|
41 | 3, 7, 1, 2, 4, 8, 9 | imasaddval 16192 |
. . . . . . . . . . . . 13
|
42 | 33, 38, 40, 41 | syl3anc 1326 |
. . . . . . . . . . . 12
|
43 | 32, 37, 42 | 3eqtr4d 2666 |
. . . . . . . . . . 11
|
44 | 3, 7, 1, 2, 4, 8, 9 | imasaddval 16192 |
. . . . . . . . . . . . 13
|
45 | 44 | 3adant3r3 1276 |
. . . . . . . . . . . 12
|
46 | 45 | oveq1d 6665 |
. . . . . . . . . . 11
|
47 | 3, 7, 1, 2, 4, 8, 9 | imasaddval 16192 |
. . . . . . . . . . . . 13
|
48 | 47 | 3adant3r1 1274 |
. . . . . . . . . . . 12
|
49 | 48 | oveq2d 6666 |
. . . . . . . . . . 11
|
50 | 43, 46, 49 | 3eqtr4d 2666 |
. . . . . . . . . 10
|
51 | | simp1 1061 |
. . . . . . . . . . . . 13
|
52 | | simp2 1062 |
. . . . . . . . . . . . 13
|
53 | 51, 52 | oveq12d 6668 |
. . . . . . . . . . . 12
|
54 | | simp3 1063 |
. . . . . . . . . . . 12
|
55 | 53, 54 | oveq12d 6668 |
. . . . . . . . . . 11
|
56 | 52, 54 | oveq12d 6668 |
. . . . . . . . . . . 12
|
57 | 51, 56 | oveq12d 6668 |
. . . . . . . . . . 11
|
58 | 55, 57 | eqeq12d 2637 |
. . . . . . . . . 10
|
59 | 50, 58 | syl5ibcom 235 |
. . . . . . . . 9
|
60 | 59 | 3exp2 1285 |
. . . . . . . 8
|
61 | 60 | imp32 449 |
. . . . . . 7
|
62 | 61 | rexlimdv 3030 |
. . . . . 6
|
63 | 62 | rexlimdvva 3038 |
. . . . 5
|
64 | 31, 63 | sylbid 230 |
. . . 4
|
65 | 64 | imp 445 |
. . 3
|
66 | | fof 6115 |
. . . . 5
|
67 | 3, 66 | syl 17 |
. . . 4
|
68 | | imasmnd2.3 |
. . . 4
|
69 | 67, 68 | ffvelrnd 6360 |
. . 3
|
70 | 23, 24 | syl 17 |
. . . . . 6
|
71 | 18, 70 | bitr3d 270 |
. . . . 5
|
72 | | simpl 473 |
. . . . . . . . 9
|
73 | 68 | adantr 481 |
. . . . . . . . 9
|
74 | | simpr 477 |
. . . . . . . . 9
|
75 | 3, 7, 1, 2, 4, 8, 9 | imasaddval 16192 |
. . . . . . . . 9
|
76 | 72, 73, 74, 75 | syl3anc 1326 |
. . . . . . . 8
|
77 | | imasmnd2.4 |
. . . . . . . 8
|
78 | 76, 77 | eqtrd 2656 |
. . . . . . 7
|
79 | | oveq2 6658 |
. . . . . . . 8
|
80 | | id 22 |
. . . . . . . 8
|
81 | 79, 80 | eqeq12d 2637 |
. . . . . . 7
|
82 | 78, 81 | syl5ibcom 235 |
. . . . . 6
|
83 | 82 | rexlimdva 3031 |
. . . . 5
|
84 | 71, 83 | sylbid 230 |
. . . 4
|
85 | 84 | imp 445 |
. . 3
|
86 | 3, 7, 1, 2, 4, 8, 9 | imasaddval 16192 |
. . . . . . . . 9
|
87 | 73, 86 | mpd3an3 1425 |
. . . . . . . 8
|
88 | | imasmnd2.5 |
. . . . . . . 8
|
89 | 87, 88 | eqtrd 2656 |
. . . . . . 7
|
90 | | oveq1 6657 |
. . . . . . . 8
|
91 | 90, 80 | eqeq12d 2637 |
. . . . . . 7
|
92 | 89, 91 | syl5ibcom 235 |
. . . . . 6
|
93 | 92 | rexlimdva 3031 |
. . . . 5
|
94 | 71, 93 | sylbid 230 |
. . . 4
|
95 | 94 | imp 445 |
. . 3
|
96 | 5, 6, 15, 65, 69, 85, 95 | ismndd 17313 |
. 2
|
97 | 5, 6, 69, 85, 95 | grpidd 17268 |
. 2
|
98 | 96, 97 | jca 554 |
1
|