Step |
Hyp |
Ref |
Expression |
1 |
|
lduallmod.d |
|
2 |
|
lduallmod.w |
|
3 |
|
lduallmod.v |
|
4 |
|
lduallmod.p |
|
5 |
|
lduallmod.f |
|
6 |
|
lduallmod.r |
|
7 |
|
lduallmod.k |
|
8 |
|
lduallmod.t |
|
9 |
|
lduallmod.o |
|
10 |
|
lduallmod.s |
|
11 |
|
eqid |
|
12 |
5 1 11 2
|
ldualvbase |
|
13 |
12
|
eqcomd |
|
14 |
|
eqidd |
|
15 |
|
eqid |
|
16 |
6 9 1 15 2
|
ldualsca |
|
17 |
16
|
eqcomd |
|
18 |
10
|
a1i |
|
19 |
9 7
|
opprbas |
|
20 |
19
|
a1i |
|
21 |
|
eqid |
|
22 |
9 21
|
oppradd |
|
23 |
22
|
a1i |
|
24 |
16
|
fveq2d |
|
25 |
|
eqid |
|
26 |
9 25
|
oppr1 |
|
27 |
26
|
a1i |
|
28 |
6
|
lmodring |
|
29 |
9
|
opprring |
|
30 |
2 28 29
|
3syl |
|
31 |
1 2
|
ldualgrp |
|
32 |
2
|
3ad2ant1 |
|
33 |
|
simp2 |
|
34 |
|
simp3 |
|
35 |
5 6 7 1 10 32 33 34
|
ldualvscl |
|
36 |
|
eqid |
|
37 |
2
|
adantr |
|
38 |
|
simpr1 |
|
39 |
|
simpr2 |
|
40 |
|
simpr3 |
|
41 |
5 6 7 1 36 10 37 38 39 40
|
ldualvsdi1 |
|
42 |
2
|
adantr |
|
43 |
|
simpr1 |
|
44 |
|
simpr2 |
|
45 |
|
simpr3 |
|
46 |
5 6 21 7 1 36 10 42 43 44 45
|
ldualvsdi2 |
|
47 |
|
eqid |
|
48 |
5 6 7 1 15 47 10 42 43 44 45
|
ldualvsass2 |
|
49 |
2
|
adantr |
|
50 |
7 25
|
ringidcl |
|
51 |
2 28 50
|
3syl |
|
52 |
51
|
adantr |
|
53 |
|
simpr |
|
54 |
5 3 6 7 8 1 10 49 52 53
|
ldualvs |
|
55 |
3 6 5 7 8 25 49 53
|
lfl1sc |
|
56 |
54 55
|
eqtrd |
|
57 |
13 14 17 18 20 23 24 27 30 31 35 41 46 48 56
|
islmodd |
|