Step |
Hyp |
Ref |
Expression |
1 |
|
linc0scn0.b |
|
2 |
|
linc0scn0.s |
|
3 |
|
linc0scn0.0 |
|
4 |
|
linc0scn0.1 |
|
5 |
|
linc0scn0.z |
|
6 |
|
linc0scn0.f |
|
7 |
|
simpl |
|
8 |
2
|
lmodring |
|
9 |
2
|
eqcomi |
|
10 |
9
|
fveq2i |
|
11 |
10 4
|
ringidcl |
|
12 |
10 3
|
ring0cl |
|
13 |
11 12
|
jca |
|
14 |
8 13
|
syl |
|
15 |
14
|
ad2antrr |
|
16 |
|
ifcl |
|
17 |
15 16
|
syl |
|
18 |
17 6
|
fmptd |
|
19 |
|
fvex |
|
20 |
19
|
a1i |
|
21 |
|
elmapg |
|
22 |
20 21
|
sylan |
|
23 |
18 22
|
mpbird |
|
24 |
1
|
pweqi |
|
25 |
24
|
eleq2i |
|
26 |
25
|
biimpi |
|
27 |
26
|
adantl |
|
28 |
|
lincval |
|
29 |
7 23 27 28
|
syl3anc |
|
30 |
|
simpr |
|
31 |
4
|
fvexi |
|
32 |
3
|
fvexi |
|
33 |
31 32
|
ifex |
|
34 |
|
eqeq1 |
|
35 |
34
|
ifbid |
|
36 |
35 6
|
fvmptg |
|
37 |
30 33 36
|
sylancl |
|
38 |
37
|
oveq1d |
|
39 |
|
ovif |
|
40 |
39
|
a1i |
|
41 |
|
oveq2 |
|
42 |
41
|
adantl |
|
43 |
|
eqid |
|
44 |
2 43 4
|
lmod1cl |
|
45 |
44
|
ancli |
|
46 |
45
|
adantr |
|
47 |
46
|
ad2antrr |
|
48 |
|
eqid |
|
49 |
2 48 43 5
|
lmodvs0 |
|
50 |
47 49
|
syl |
|
51 |
42 50
|
eqtrd |
|
52 |
7
|
adantr |
|
53 |
|
elelpwi |
|
54 |
53
|
expcom |
|
55 |
54
|
adantl |
|
56 |
55
|
imp |
|
57 |
1 2 48 3 5
|
lmod0vs |
|
58 |
52 56 57
|
syl2anc |
|
59 |
58
|
adantr |
|
60 |
51 59
|
ifeqda |
|
61 |
38 40 60
|
3eqtrd |
|
62 |
61
|
mpteq2dva |
|
63 |
62
|
oveq2d |
|
64 |
|
lmodgrp |
|
65 |
64
|
grpmndd |
|
66 |
5
|
gsumz |
|
67 |
65 66
|
sylan |
|
68 |
29 63 67
|
3eqtrd |
|