Step |
Hyp |
Ref |
Expression |
1 |
|
linc1.b |
|
2 |
|
linc1.s |
|
3 |
|
linc1.0 |
|
4 |
|
linc1.1 |
|
5 |
|
linc1.f |
|
6 |
|
simp1 |
|
7 |
2
|
lmodring |
|
8 |
2
|
eqcomi |
|
9 |
8
|
fveq2i |
|
10 |
9 4
|
ringidcl |
|
11 |
9 3
|
ring0cl |
|
12 |
10 11
|
jca |
|
13 |
7 12
|
syl |
|
14 |
13
|
3ad2ant1 |
|
15 |
14
|
adantr |
|
16 |
|
ifcl |
|
17 |
15 16
|
syl |
|
18 |
17 5
|
fmptd |
|
19 |
|
fvex |
|
20 |
|
simp2 |
|
21 |
|
elmapg |
|
22 |
19 20 21
|
sylancr |
|
23 |
18 22
|
mpbird |
|
24 |
1
|
pweqi |
|
25 |
24
|
eleq2i |
|
26 |
25
|
biimpi |
|
27 |
26
|
3ad2ant2 |
|
28 |
|
lincval |
|
29 |
6 23 27 28
|
syl3anc |
|
30 |
|
eqid |
|
31 |
|
lmodgrp |
|
32 |
|
grpmnd |
|
33 |
31 32
|
syl |
|
34 |
33
|
3ad2ant1 |
|
35 |
|
simp3 |
|
36 |
6
|
adantr |
|
37 |
|
eqeq1 |
|
38 |
37
|
ifbid |
|
39 |
|
simpr |
|
40 |
|
eqid |
|
41 |
2 40 4
|
lmod1cl |
|
42 |
41
|
3ad2ant1 |
|
43 |
42
|
adantr |
|
44 |
2 40 3
|
lmod0cl |
|
45 |
44
|
3ad2ant1 |
|
46 |
45
|
adantr |
|
47 |
43 46
|
ifcld |
|
48 |
5 38 39 47
|
fvmptd3 |
|
49 |
48 47
|
eqeltrd |
|
50 |
|
elelpwi |
|
51 |
50
|
expcom |
|
52 |
51
|
3ad2ant2 |
|
53 |
52
|
imp |
|
54 |
|
eqid |
|
55 |
1 2 54 40
|
lmodvscl |
|
56 |
36 49 53 55
|
syl3anc |
|
57 |
|
eqid |
|
58 |
56 57
|
fmptd |
|
59 |
|
fveq2 |
|
60 |
|
id |
|
61 |
59 60
|
oveq12d |
|
62 |
61
|
cbvmptv |
|
63 |
|
fvexd |
|
64 |
|
ovexd |
|
65 |
62 20 63 64
|
mptsuppd |
|
66 |
|
2a1 |
|
67 |
|
simprr |
|
68 |
4
|
fvexi |
|
69 |
3
|
fvexi |
|
70 |
68 69
|
ifex |
|
71 |
|
eqeq1 |
|
72 |
71
|
ifbid |
|
73 |
72 5
|
fvmptg |
|
74 |
67 70 73
|
sylancl |
|
75 |
|
iffalse |
|
76 |
75
|
adantr |
|
77 |
74 76
|
eqtrd |
|
78 |
77
|
oveq1d |
|
79 |
6
|
adantr |
|
80 |
79
|
adantl |
|
81 |
|
elelpwi |
|
82 |
81
|
expcom |
|
83 |
82
|
3ad2ant2 |
|
84 |
83
|
imp |
|
85 |
84
|
adantl |
|
86 |
1 2 54 3 30
|
lmod0vs |
|
87 |
80 85 86
|
syl2anc |
|
88 |
78 87
|
eqtrd |
|
89 |
88
|
neeq1d |
|
90 |
|
eqneqall |
|
91 |
30 90
|
ax-mp |
|
92 |
89 91
|
syl6bi |
|
93 |
92
|
ex |
|
94 |
66 93
|
pm2.61i |
|
95 |
94
|
ralrimiva |
|
96 |
|
rabsssn |
|
97 |
95 96
|
sylibr |
|
98 |
65 97
|
eqsstrd |
|
99 |
1 30 34 20 35 58 98
|
gsumpt |
|
100 |
|
ovex |
|
101 |
|
fveq2 |
|
102 |
|
id |
|
103 |
101 102
|
oveq12d |
|
104 |
103 57
|
fvmptg |
|
105 |
35 100 104
|
sylancl |
|
106 |
|
iftrue |
|
107 |
106 5
|
fvmptg |
|
108 |
35 68 107
|
sylancl |
|
109 |
108
|
oveq1d |
|
110 |
|
elelpwi |
|
111 |
110
|
ancoms |
|
112 |
111
|
3adant1 |
|
113 |
1 2 54 4
|
lmodvs1 |
|
114 |
6 112 113
|
syl2anc |
|
115 |
105 109 114
|
3eqtrd |
|
116 |
29 99 115
|
3eqtrd |
|