Step | Hyp | Ref
| Expression |
1 | | assalmod 19319 |
. . . 4
AssAlg |
2 | | assaring 19320 |
. . . 4
AssAlg |
3 | 1, 2 | jca 554 |
. . 3
AssAlg |
4 | 3 | a1i 11 |
. 2
AssAlg |
5 | | assalmod 19319 |
. . . 4
AssAlg |
6 | | assapropd.1 |
. . . . 5
|
7 | | assapropd.2 |
. . . . 5
|
8 | | assapropd.3 |
. . . . 5
|
9 | | assapropd.5 |
. . . . 5
Scalar |
10 | | assapropd.6 |
. . . . 5
Scalar |
11 | | assapropd.7 |
. . . . 5
|
12 | | assapropd.8 |
. . . . 5
|
13 | 6, 7, 8, 9, 10, 11, 12 | lmodpropd 18926 |
. . . 4
|
14 | 5, 13 | syl5ibr 236 |
. . 3
AssAlg |
15 | | assaring 19320 |
. . . 4
AssAlg |
16 | | assapropd.4 |
. . . . 5
|
17 | 6, 7, 8, 16 | ringpropd 18582 |
. . . 4
|
18 | 15, 17 | syl5ibr 236 |
. . 3
AssAlg |
19 | 14, 18 | jcad 555 |
. 2
AssAlg |
20 | 9, 10 | eqtr3d 2658 |
. . . . . . . 8
Scalar Scalar |
21 | 20 | eleq1d 2686 |
. . . . . . 7
Scalar
Scalar |
22 | 13, 17, 21 | 3anbi123d 1399 |
. . . . . 6
Scalar
Scalar |
23 | 22 | adantr 481 |
. . . . 5
Scalar Scalar |
24 | | simpll 790 |
. . . . . . . . . . . . 13
|
25 | | simplrl 800 |
. . . . . . . . . . . . . . 15
|
26 | | simprl 794 |
. . . . . . . . . . . . . . . 16
|
27 | 9 | fveq2d 6195 |
. . . . . . . . . . . . . . . . . 18
Scalar |
28 | 11, 27 | syl5eq 2668 |
. . . . . . . . . . . . . . . . 17
Scalar |
29 | 24, 28 | syl 17 |
. . . . . . . . . . . . . . . 16
Scalar |
30 | 26, 29 | eleqtrd 2703 |
. . . . . . . . . . . . . . 15
Scalar |
31 | | simprrl 804 |
. . . . . . . . . . . . . . . 16
|
32 | 24, 6 | syl 17 |
. . . . . . . . . . . . . . . 16
|
33 | 31, 32 | eleqtrd 2703 |
. . . . . . . . . . . . . . 15
|
34 | | eqid 2622 |
. . . . . . . . . . . . . . . 16
|
35 | | eqid 2622 |
. . . . . . . . . . . . . . . 16
Scalar Scalar |
36 | | eqid 2622 |
. . . . . . . . . . . . . . . 16
|
37 | | eqid 2622 |
. . . . . . . . . . . . . . . 16
Scalar Scalar |
38 | 34, 35, 36, 37 | lmodvscl 18880 |
. . . . . . . . . . . . . . 15
Scalar
|
39 | 25, 30, 33, 38 | syl3anc 1326 |
. . . . . . . . . . . . . 14
|
40 | 39, 32 | eleqtrrd 2704 |
. . . . . . . . . . . . 13
|
41 | | simprrr 805 |
. . . . . . . . . . . . 13
|
42 | 16 | oveqrspc2v 6673 |
. . . . . . . . . . . . 13
|
43 | 24, 40, 41, 42 | syl12anc 1324 |
. . . . . . . . . . . 12
|
44 | 12 | oveqrspc2v 6673 |
. . . . . . . . . . . . . 14
|
45 | 24, 26, 31, 44 | syl12anc 1324 |
. . . . . . . . . . . . 13
|
46 | 45 | oveq1d 6665 |
. . . . . . . . . . . 12
|
47 | 43, 46 | eqtrd 2656 |
. . . . . . . . . . 11
|
48 | | simplrr 801 |
. . . . . . . . . . . . . . 15
|
49 | 41, 32 | eleqtrd 2703 |
. . . . . . . . . . . . . . 15
|
50 | | eqid 2622 |
. . . . . . . . . . . . . . . 16
|
51 | 34, 50 | ringcl 18561 |
. . . . . . . . . . . . . . 15
|
52 | 48, 33, 49, 51 | syl3anc 1326 |
. . . . . . . . . . . . . 14
|
53 | 52, 32 | eleqtrrd 2704 |
. . . . . . . . . . . . 13
|
54 | 12 | oveqrspc2v 6673 |
. . . . . . . . . . . . 13
|
55 | 24, 26, 53, 54 | syl12anc 1324 |
. . . . . . . . . . . 12
|
56 | 16 | oveqrspc2v 6673 |
. . . . . . . . . . . . . 14
|
57 | 24, 31, 41, 56 | syl12anc 1324 |
. . . . . . . . . . . . 13
|
58 | 57 | oveq2d 6666 |
. . . . . . . . . . . 12
|
59 | 55, 58 | eqtrd 2656 |
. . . . . . . . . . 11
|
60 | 47, 59 | eqeq12d 2637 |
. . . . . . . . . 10
|
61 | 34, 35, 36, 37 | lmodvscl 18880 |
. . . . . . . . . . . . . . 15
Scalar
|
62 | 25, 30, 49, 61 | syl3anc 1326 |
. . . . . . . . . . . . . 14
|
63 | 62, 32 | eleqtrrd 2704 |
. . . . . . . . . . . . 13
|
64 | 16 | oveqrspc2v 6673 |
. . . . . . . . . . . . 13
|
65 | 24, 31, 63, 64 | syl12anc 1324 |
. . . . . . . . . . . 12
|
66 | 12 | oveqrspc2v 6673 |
. . . . . . . . . . . . . 14
|
67 | 24, 26, 41, 66 | syl12anc 1324 |
. . . . . . . . . . . . 13
|
68 | 67 | oveq2d 6666 |
. . . . . . . . . . . 12
|
69 | 65, 68 | eqtrd 2656 |
. . . . . . . . . . 11
|
70 | 69, 59 | eqeq12d 2637 |
. . . . . . . . . 10
|
71 | 60, 70 | anbi12d 747 |
. . . . . . . . 9
|
72 | 71 | anassrs 680 |
. . . . . . . 8
|
73 | 72 | 2ralbidva 2988 |
. . . . . . 7
|
74 | 73 | ralbidva 2985 |
. . . . . 6
|
75 | 28 | adantr 481 |
. . . . . . 7
Scalar |
76 | 6 | adantr 481 |
. . . . . . . 8
|
77 | 76 | raleqdv 3144 |
. . . . . . . 8
|
78 | 76, 77 | raleqbidv 3152 |
. . . . . . 7
|
79 | 75, 78 | raleqbidv 3152 |
. . . . . 6
Scalar |
80 | 10 | fveq2d 6195 |
. . . . . . . . 9
Scalar |
81 | 11, 80 | syl5eq 2668 |
. . . . . . . 8
Scalar |
82 | 81 | adantr 481 |
. . . . . . 7
Scalar |
83 | 7 | adantr 481 |
. . . . . . . 8
|
84 | 83 | raleqdv 3144 |
. . . . . . . 8
|
85 | 83, 84 | raleqbidv 3152 |
. . . . . . 7
|
86 | 82, 85 | raleqbidv 3152 |
. . . . . 6
Scalar |
87 | 74, 79, 86 | 3bitr3d 298 |
. . . . 5
Scalar
Scalar
|
88 | 23, 87 | anbi12d 747 |
. . . 4
Scalar
Scalar
Scalar Scalar |
89 | 34, 35, 37, 36, 50 | isassa 19315 |
. . . 4
AssAlg Scalar
Scalar |
90 | | eqid 2622 |
. . . . 5
|
91 | | eqid 2622 |
. . . . 5
Scalar Scalar |
92 | | eqid 2622 |
. . . . 5
Scalar Scalar |
93 | | eqid 2622 |
. . . . 5
|
94 | | eqid 2622 |
. . . . 5
|
95 | 90, 91, 92, 93, 94 | isassa 19315 |
. . . 4
AssAlg Scalar
Scalar |
96 | 88, 89, 95 | 3bitr4g 303 |
. . 3
AssAlg
AssAlg |
97 | 96 | ex 450 |
. 2
AssAlg AssAlg |
98 | 4, 19, 97 | pm5.21ndd 369 |
1
AssAlg
AssAlg |