Step |
Hyp |
Ref |
Expression |
1 |
|
lspsolv.v |
|
2 |
|
lspsolv.s |
|
3 |
|
lspsolv.n |
|
4 |
|
eqid |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
|
lveclmod |
|
10 |
9
|
adantr |
|
11 |
|
simpr1 |
|
12 |
|
simpr2 |
|
13 |
|
simpr3 |
|
14 |
13
|
eldifad |
|
15 |
1 2 3 4 5 6 7 8 10 11 12 14
|
lspsolvlem |
|
16 |
4
|
lvecdrng |
|
17 |
16
|
ad2antrr |
|
18 |
|
simprl |
|
19 |
10
|
adantr |
|
20 |
12
|
adantr |
|
21 |
|
eqid |
|
22 |
|
eqid |
|
23 |
1 4 7 21 22
|
lmod0vs |
|
24 |
19 20 23
|
syl2anc |
|
25 |
24
|
oveq2d |
|
26 |
11
|
adantr |
|
27 |
20
|
snssd |
|
28 |
26 27
|
unssd |
|
29 |
1 3
|
lspssv |
|
30 |
19 28 29
|
syl2anc |
|
31 |
30
|
ssdifssd |
|
32 |
13
|
adantr |
|
33 |
31 32
|
sseldd |
|
34 |
1 6 22
|
lmod0vrid |
|
35 |
19 33 34
|
syl2anc |
|
36 |
25 35
|
eqtrd |
|
37 |
36 32
|
eqeltrd |
|
38 |
37
|
eldifbd |
|
39 |
|
simprr |
|
40 |
|
oveq1 |
|
41 |
40
|
oveq2d |
|
42 |
41
|
eleq1d |
|
43 |
39 42
|
syl5ibcom |
|
44 |
43
|
necon3bd |
|
45 |
38 44
|
mpd |
|
46 |
|
eqid |
|
47 |
|
eqid |
|
48 |
|
eqid |
|
49 |
5 21 46 47 48
|
drnginvrl |
|
50 |
17 18 45 49
|
syl3anc |
|
51 |
50
|
oveq1d |
|
52 |
5 21 48
|
drnginvrcl |
|
53 |
17 18 45 52
|
syl3anc |
|
54 |
1 4 7 5 46
|
lmodvsass |
|
55 |
19 53 18 20 54
|
syl13anc |
|
56 |
1 4 7 47
|
lmodvs1 |
|
57 |
19 20 56
|
syl2anc |
|
58 |
51 55 57
|
3eqtr3d |
|
59 |
33
|
snssd |
|
60 |
26 59
|
unssd |
|
61 |
1 2 3
|
lspcl |
|
62 |
19 60 61
|
syl2anc |
|
63 |
1 4 7 5
|
lmodvscl |
|
64 |
19 18 20 63
|
syl3anc |
|
65 |
|
eqid |
|
66 |
1 6 65
|
lmodvpncan |
|
67 |
19 64 33 66
|
syl3anc |
|
68 |
1 6
|
lmodcom |
|
69 |
19 64 33 68
|
syl3anc |
|
70 |
|
ssun1 |
|
71 |
70
|
a1i |
|
72 |
1 3
|
lspss |
|
73 |
19 60 71 72
|
syl3anc |
|
74 |
73 39
|
sseldd |
|
75 |
69 74
|
eqeltrd |
|
76 |
1 3
|
lspssid |
|
77 |
19 60 76
|
syl2anc |
|
78 |
|
snidg |
|
79 |
|
elun2 |
|
80 |
33 78 79
|
3syl |
|
81 |
77 80
|
sseldd |
|
82 |
65 2
|
lssvsubcl |
|
83 |
19 62 75 81 82
|
syl22anc |
|
84 |
67 83
|
eqeltrrd |
|
85 |
4 7 5 2
|
lssvscl |
|
86 |
19 62 53 84 85
|
syl22anc |
|
87 |
58 86
|
eqeltrrd |
|
88 |
15 87
|
rexlimddv |
|