Step |
Hyp |
Ref |
Expression |
1 |
|
lincresunit.b |
|
2 |
|
lincresunit.r |
|
3 |
|
lincresunit.e |
|
4 |
|
lincresunit.u |
|
5 |
|
lincresunit.0 |
|
6 |
|
lincresunit.z |
|
7 |
|
lincresunit.n |
|
8 |
|
lincresunit.i |
|
9 |
|
lincresunit.t |
|
10 |
|
lincresunit.g |
|
11 |
|
simp2 |
|
12 |
11
|
3ad2ant1 |
|
13 |
|
simp1 |
|
14 |
|
3simpa |
|
15 |
14
|
3ad2ant2 |
|
16 |
13 15
|
jca |
|
17 |
|
eldifi |
|
18 |
1 2 3 4 5 6 7 8 9 10
|
lincresunitlem2 |
|
19 |
16 17 18
|
syl2an |
|
20 |
2
|
fveq2i |
|
21 |
3 20
|
eqtri |
|
22 |
19 21
|
eleqtrdi |
|
23 |
22 10
|
fmptd |
|
24 |
|
fvex |
|
25 |
|
difexg |
|
26 |
25
|
3ad2ant1 |
|
27 |
26
|
3ad2ant1 |
|
28 |
|
elmapg |
|
29 |
24 27 28
|
sylancr |
|
30 |
23 29
|
mpbird |
|
31 |
|
difexg |
|
32 |
31
|
adantl |
|
33 |
|
ssdifss |
|
34 |
33
|
a1i |
|
35 |
|
elpwi |
|
36 |
34 35
|
impel |
|
37 |
32 36
|
elpwd |
|
38 |
37
|
expcom |
|
39 |
1
|
pweqi |
|
40 |
38 39
|
eleq2s |
|
41 |
40
|
imp |
|
42 |
41
|
3adant2 |
|
43 |
42
|
3ad2ant1 |
|
44 |
|
lincval |
|
45 |
12 30 43 44
|
syl3anc |
|
46 |
|
simp1 |
|
47 |
|
simp3 |
|
48 |
11 46 47
|
3jca |
|
49 |
48
|
adantr |
|
50 |
|
3simpb |
|
51 |
50
|
adantl |
|
52 |
|
eqidd |
|
53 |
|
eqid |
|
54 |
|
eqid |
|
55 |
1 2 3 53 54 5
|
lincdifsn |
|
56 |
49 51 52 55
|
syl3anc |
|
57 |
56
|
eqeq1d |
|
58 |
|
fveq2 |
|
59 |
|
id |
|
60 |
58 59
|
oveq12d |
|
61 |
60
|
cbvmptv |
|
62 |
61
|
a1i |
|
63 |
62
|
oveq2d |
|
64 |
63
|
oveq2d |
|
65 |
1 2 3 4 5 6 7 8 9 10
|
lincresunit3lem2 |
|
66 |
64 65
|
eqtr2d |
|
67 |
66
|
oveq1d |
|
68 |
67
|
eqeq1d |
|
69 |
|
lmodgrp |
|
70 |
69
|
3ad2ant2 |
|
71 |
70
|
adantr |
|
72 |
11
|
adantr |
|
73 |
|
elmapi |
|
74 |
73
|
3ad2ant1 |
|
75 |
|
ffvelrn |
|
76 |
74 47 75
|
syl2anr |
|
77 |
|
elpwi |
|
78 |
77
|
sselda |
|
79 |
78
|
3adant2 |
|
80 |
79
|
adantr |
|
81 |
1 2 53 3
|
lmodvscl |
|
82 |
72 76 80 81
|
syl3anc |
|
83 |
2
|
lmodfgrp |
|
84 |
83
|
3ad2ant2 |
|
85 |
3 7
|
grpinvcl |
|
86 |
84 76 85
|
syl2an2r |
|
87 |
|
lmodcmn |
|
88 |
87
|
3ad2ant2 |
|
89 |
88
|
adantr |
|
90 |
26
|
adantr |
|
91 |
|
simpll2 |
|
92 |
1 2 3 4 5 6 7 8 9 10
|
lincresunit1 |
|
93 |
92
|
3adantr3 |
|
94 |
|
elmapi |
|
95 |
93 94
|
syl |
|
96 |
95
|
ffvelrnda |
|
97 |
|
ssel2 |
|
98 |
97
|
expcom |
|
99 |
17 77 98
|
syl2imc |
|
100 |
99
|
3ad2ant1 |
|
101 |
100
|
adantr |
|
102 |
101
|
imp |
|
103 |
1 2 53 3
|
lmodvscl |
|
104 |
91 96 102 103
|
syl3anc |
|
105 |
104
|
fmpttd |
|
106 |
25
|
adantr |
|
107 |
|
ssdifss |
|
108 |
77 107
|
syl |
|
109 |
108
|
adantr |
|
110 |
109 1
|
sseqtrdi |
|
111 |
106 110
|
elpwd |
|
112 |
111
|
3adant2 |
|
113 |
11 112
|
jca |
|
114 |
113
|
adantr |
|
115 |
1 2 3 4 5 6 7 8 9 10
|
lincresunit2 |
|
116 |
115 5
|
breqtrdi |
|
117 |
2 3
|
scmfsupp |
|
118 |
114 93 116 117
|
syl3anc |
|
119 |
118 6
|
breqtrrdi |
|
120 |
1 6 89 90 105 119
|
gsumcl |
|
121 |
1 2 53 3
|
lmodvscl |
|
122 |
72 86 120 121
|
syl3anc |
|
123 |
|
eqid |
|
124 |
1 54 6 123
|
grpinvid2 |
|
125 |
71 82 122 124
|
syl3anc |
|
126 |
1 2 53 123 3 7 72 80 76
|
lmodvsneg |
|
127 |
126
|
eqeq1d |
|
128 |
|
simpr2 |
|
129 |
1 2 3 4 7 53
|
lincresunit3lem3 |
|
130 |
|
eqcom |
|
131 |
129 130
|
syl6bb |
|
132 |
72 80 120 128 131
|
syl31anc |
|
133 |
132
|
biimpd |
|
134 |
127 133
|
sylbid |
|
135 |
125 134
|
sylbird |
|
136 |
68 135
|
sylbid |
|
137 |
57 136
|
sylbid |
|
138 |
137
|
3impia |
|
139 |
45 138
|
eqtrd |
|