Step |
Hyp |
Ref |
Expression |
1 |
|
lkrlsp.d |
|
2 |
|
lkrlsp.o |
|
3 |
|
lkrlsp.v |
|
4 |
|
lkrlsp.n |
|
5 |
|
lkrlsp.p |
|
6 |
|
lkrlsp.f |
|
7 |
|
lkrlsp.k |
|
8 |
|
lveclmod |
|
9 |
8
|
3ad2ant1 |
|
10 |
|
simp2r |
|
11 |
|
eqid |
|
12 |
6 7 11
|
lkrlss |
|
13 |
9 10 12
|
syl2anc |
|
14 |
|
simp2l |
|
15 |
3 11 4
|
lspsncl |
|
16 |
9 14 15
|
syl2anc |
|
17 |
11 5
|
lsmcl |
|
18 |
9 13 16 17
|
syl3anc |
|
19 |
3 11
|
lssss |
|
20 |
18 19
|
syl |
|
21 |
|
simpl1 |
|
22 |
21 8
|
syl |
|
23 |
|
simpr |
|
24 |
1
|
lmodring |
|
25 |
22 24
|
syl |
|
26 |
|
simpl2r |
|
27 |
|
eqid |
|
28 |
1 27 3 6
|
lflcl |
|
29 |
21 26 23 28
|
syl3anc |
|
30 |
1
|
lvecdrng |
|
31 |
21 30
|
syl |
|
32 |
|
simpl2l |
|
33 |
1 27 3 6
|
lflcl |
|
34 |
21 26 32 33
|
syl3anc |
|
35 |
|
simpl3 |
|
36 |
|
eqid |
|
37 |
27 2 36
|
drnginvrcl |
|
38 |
31 34 35 37
|
syl3anc |
|
39 |
|
eqid |
|
40 |
27 39
|
ringcl |
|
41 |
25 29 38 40
|
syl3anc |
|
42 |
|
eqid |
|
43 |
3 1 42 27
|
lmodvscl |
|
44 |
22 41 32 43
|
syl3anc |
|
45 |
|
eqid |
|
46 |
|
eqid |
|
47 |
3 45 46
|
lmodvnpcan |
|
48 |
22 23 44 47
|
syl3anc |
|
49 |
11
|
lsssssubg |
|
50 |
22 49
|
syl |
|
51 |
13
|
adantr |
|
52 |
50 51
|
sseldd |
|
53 |
16
|
adantr |
|
54 |
50 53
|
sseldd |
|
55 |
3 46
|
lmodvsubcl |
|
56 |
22 23 44 55
|
syl3anc |
|
57 |
|
eqid |
|
58 |
1 57 3 46 6
|
lflsub |
|
59 |
22 26 23 44 58
|
syl112anc |
|
60 |
1 27 39 3 42 6
|
lflmul |
|
61 |
22 26 41 32 60
|
syl112anc |
|
62 |
27 39
|
ringass |
|
63 |
25 29 38 34 62
|
syl13anc |
|
64 |
|
eqid |
|
65 |
27 2 39 64 36
|
drnginvrl |
|
66 |
31 34 35 65
|
syl3anc |
|
67 |
66
|
oveq2d |
|
68 |
27 39 64
|
ringridm |
|
69 |
25 29 68
|
syl2anc |
|
70 |
67 69
|
eqtrd |
|
71 |
61 63 70
|
3eqtrd |
|
72 |
71
|
oveq2d |
|
73 |
1
|
lmodfgrp |
|
74 |
22 73
|
syl |
|
75 |
27 2 57
|
grpsubid |
|
76 |
74 29 75
|
syl2anc |
|
77 |
59 72 76
|
3eqtrd |
|
78 |
3 1 2 6 7
|
ellkr |
|
79 |
21 26 78
|
syl2anc |
|
80 |
56 77 79
|
mpbir2and |
|
81 |
3 42 1 27 4 22 41 32
|
lspsneli |
|
82 |
45 5
|
lsmelvali |
|
83 |
52 54 80 81 82
|
syl22anc |
|
84 |
48 83
|
eqeltrrd |
|
85 |
20 84
|
eqelssd |
|