Step | Hyp | Ref
| Expression |
1 | | dchrmhm.g |
. . 3
DChr |
2 | | dchrmhm.z |
. . 3
ℤ/nℤ |
3 | | dchrmhm.b |
. . 3
|
4 | | dchrmul.t |
. . 3
|
5 | | dchrmul.x |
. . 3
|
6 | | dchrmul.y |
. . 3
|
7 | 1, 2, 3, 4, 5, 6 | dchrmul 24973 |
. 2
|
8 | | mulcl 10020 |
. . . . 5
|
9 | 8 | adantl 482 |
. . . 4
|
10 | | eqid 2622 |
. . . . 5
|
11 | 1, 2, 3, 10, 5 | dchrf 24967 |
. . . 4
|
12 | 1, 2, 3, 10, 6 | dchrf 24967 |
. . . 4
|
13 | | fvexd 6203 |
. . . 4
|
14 | | inidm 3822 |
. . . 4
|
15 | 9, 11, 12, 13, 13, 14 | off 6912 |
. . 3
|
16 | | eqid 2622 |
. . . . . . . 8
Unit Unit |
17 | 10, 16 | unitcl 18659 |
. . . . . . 7
Unit
|
18 | 10, 16 | unitcl 18659 |
. . . . . . 7
Unit
|
19 | 17, 18 | anim12i 590 |
. . . . . 6
Unit Unit
|
20 | 1, 3 | dchrrcl 24965 |
. . . . . . . . . . . . . 14
|
21 | 5, 20 | syl 17 |
. . . . . . . . . . . . 13
|
22 | 1, 2, 10, 16, 21, 3 | dchrelbas2 24962 |
. . . . . . . . . . . 12
mulGrp MndHom mulGrpℂfld
Unit |
23 | 5, 22 | mpbid 222 |
. . . . . . . . . . 11
mulGrp MndHom mulGrpℂfld
Unit |
24 | 23 | simpld 475 |
. . . . . . . . . 10
mulGrp MndHom mulGrpℂfld |
25 | | eqid 2622 |
. . . . . . . . . . . . 13
mulGrp mulGrp |
26 | 25, 10 | mgpbas 18495 |
. . . . . . . . . . . 12
mulGrp |
27 | | eqid 2622 |
. . . . . . . . . . . . 13
|
28 | 25, 27 | mgpplusg 18493 |
. . . . . . . . . . . 12
mulGrp |
29 | | eqid 2622 |
. . . . . . . . . . . . 13
mulGrpℂfld mulGrpℂfld |
30 | | cnfldmul 19752 |
. . . . . . . . . . . . 13
ℂfld |
31 | 29, 30 | mgpplusg 18493 |
. . . . . . . . . . . 12
mulGrpℂfld |
32 | 26, 28, 31 | mhmlin 17342 |
. . . . . . . . . . 11
mulGrp MndHom mulGrpℂfld
|
33 | 32 | 3expb 1266 |
. . . . . . . . . 10
mulGrp MndHom mulGrpℂfld
|
34 | 24, 33 | sylan 488 |
. . . . . . . . 9
|
35 | 1, 2, 10, 16, 21, 3 | dchrelbas2 24962 |
. . . . . . . . . . . 12
mulGrp MndHom mulGrpℂfld
Unit |
36 | 6, 35 | mpbid 222 |
. . . . . . . . . . 11
mulGrp MndHom mulGrpℂfld
Unit |
37 | 36 | simpld 475 |
. . . . . . . . . 10
mulGrp MndHom mulGrpℂfld |
38 | 26, 28, 31 | mhmlin 17342 |
. . . . . . . . . . 11
mulGrp MndHom mulGrpℂfld
|
39 | 38 | 3expb 1266 |
. . . . . . . . . 10
mulGrp MndHom mulGrpℂfld
|
40 | 37, 39 | sylan 488 |
. . . . . . . . 9
|
41 | 34, 40 | oveq12d 6668 |
. . . . . . . 8
|
42 | 11 | ffvelrnda 6359 |
. . . . . . . . . 10
|
43 | 42 | adantrr 753 |
. . . . . . . . 9
|
44 | | simpr 477 |
. . . . . . . . . 10
|
45 | | ffvelrn 6357 |
. . . . . . . . . 10
|
46 | 11, 44, 45 | syl2an 494 |
. . . . . . . . 9
|
47 | 12 | ffvelrnda 6359 |
. . . . . . . . . 10
|
48 | 47 | adantrr 753 |
. . . . . . . . 9
|
49 | | ffvelrn 6357 |
. . . . . . . . . 10
|
50 | 12, 44, 49 | syl2an 494 |
. . . . . . . . 9
|
51 | 43, 46, 48, 50 | mul4d 10248 |
. . . . . . . 8
|
52 | 41, 51 | eqtrd 2656 |
. . . . . . 7
|
53 | | ffn 6045 |
. . . . . . . . . 10
|
54 | 11, 53 | syl 17 |
. . . . . . . . 9
|
55 | 54 | adantr 481 |
. . . . . . . 8
|
56 | | ffn 6045 |
. . . . . . . . . 10
|
57 | 12, 56 | syl 17 |
. . . . . . . . 9
|
58 | 57 | adantr 481 |
. . . . . . . 8
|
59 | | fvexd 6203 |
. . . . . . . 8
|
60 | 21 | nnnn0d 11351 |
. . . . . . . . . 10
|
61 | 2 | zncrng 19893 |
. . . . . . . . . 10
|
62 | | crngring 18558 |
. . . . . . . . . 10
|
63 | 60, 61, 62 | 3syl 18 |
. . . . . . . . 9
|
64 | 10, 27 | ringcl 18561 |
. . . . . . . . . 10
|
65 | 64 | 3expb 1266 |
. . . . . . . . 9
|
66 | 63, 65 | sylan 488 |
. . . . . . . 8
|
67 | | fnfvof 6911 |
. . . . . . . 8
|
68 | 55, 58, 59, 66, 67 | syl22anc 1327 |
. . . . . . 7
|
69 | 54 | adantr 481 |
. . . . . . . . . 10
|
70 | 57 | adantr 481 |
. . . . . . . . . 10
|
71 | | fvexd 6203 |
. . . . . . . . . 10
|
72 | | simpr 477 |
. . . . . . . . . 10
|
73 | | fnfvof 6911 |
. . . . . . . . . 10
|
74 | 69, 70, 71, 72, 73 | syl22anc 1327 |
. . . . . . . . 9
|
75 | 74 | adantrr 753 |
. . . . . . . 8
|
76 | | simprr 796 |
. . . . . . . . 9
|
77 | | fnfvof 6911 |
. . . . . . . . 9
|
78 | 55, 58, 59, 76, 77 | syl22anc 1327 |
. . . . . . . 8
|
79 | 75, 78 | oveq12d 6668 |
. . . . . . 7
|
80 | 52, 68, 79 | 3eqtr4d 2666 |
. . . . . 6
|
81 | 19, 80 | sylan2 491 |
. . . . 5
Unit
Unit |
82 | 81 | ralrimivva 2971 |
. . . 4
Unit Unit
|
83 | | eqid 2622 |
. . . . . . . 8
|
84 | 10, 83 | ringidcl 18568 |
. . . . . . 7
|
85 | 63, 84 | syl 17 |
. . . . . 6
|
86 | | fnfvof 6911 |
. . . . . 6
|
87 | 54, 57, 13, 85, 86 | syl22anc 1327 |
. . . . 5
|
88 | 25, 83 | ringidval 18503 |
. . . . . . . . 9
mulGrp |
89 | | cnfld1 19771 |
. . . . . . . . . 10
ℂfld |
90 | 29, 89 | ringidval 18503 |
. . . . . . . . 9
mulGrpℂfld |
91 | 88, 90 | mhm0 17343 |
. . . . . . . 8
mulGrp
MndHom mulGrpℂfld |
92 | 24, 91 | syl 17 |
. . . . . . 7
|
93 | 88, 90 | mhm0 17343 |
. . . . . . . 8
mulGrp
MndHom mulGrpℂfld |
94 | 37, 93 | syl 17 |
. . . . . . 7
|
95 | 92, 94 | oveq12d 6668 |
. . . . . 6
|
96 | | 1t1e1 11175 |
. . . . . 6
|
97 | 95, 96 | syl6eq 2672 |
. . . . 5
|
98 | 87, 97 | eqtrd 2656 |
. . . 4
|
99 | 74 | neeq1d 2853 |
. . . . . . 7
|
100 | 42, 47 | mulne0bd 10678 |
. . . . . . 7
|
101 | 99, 100 | bitr4d 271 |
. . . . . 6
|
102 | 23 | simprd 479 |
. . . . . . . 8
Unit |
103 | 102 | r19.21bi 2932 |
. . . . . . 7
Unit |
104 | 103 | adantrd 484 |
. . . . . 6
Unit |
105 | 101, 104 | sylbid 230 |
. . . . 5
Unit |
106 | 105 | ralrimiva 2966 |
. . . 4
Unit |
107 | 82, 98, 106 | 3jca 1242 |
. . 3
Unit
Unit
Unit |
108 | 1, 2, 10, 16, 21, 3 | dchrelbas3 24963 |
. . 3
Unit Unit
Unit |
109 | 15, 107, 108 | mpbir2and 957 |
. 2
|
110 | 7, 109 | eqeltrd 2701 |
1
|