Step |
Hyp |
Ref |
Expression |
1 |
|
lsmcss.c |
|
2 |
|
lsmcss.j |
|
3 |
|
lsmcss.o |
|
4 |
|
lsmcss.p |
|
5 |
|
lsmcss.1 |
|
6 |
|
lsmcss.2 |
|
7 |
|
lsmcss.3 |
|
8 |
7
|
sseld |
|
9 |
|
phllmod |
|
10 |
5 9
|
syl |
|
11 |
2 3
|
ocvss |
|
12 |
11
|
a1i |
|
13 |
|
eqid |
|
14 |
2 13 4
|
lsmelvalx |
|
15 |
10 6 12 14
|
syl3anc |
|
16 |
8 15
|
sylibd |
|
17 |
5
|
ad2antrr |
|
18 |
6
|
ad2antrr |
|
19 |
|
simplrl |
|
20 |
18 19
|
sseldd |
|
21 |
|
simplrr |
|
22 |
11 21
|
sseldi |
|
23 |
|
eqid |
|
24 |
|
eqid |
|
25 |
|
eqid |
|
26 |
23 24 2 13 25
|
ipdir |
|
27 |
17 20 22 22 26
|
syl13anc |
|
28 |
|
eqid |
|
29 |
2 24 23 28 3
|
ocvi |
|
30 |
21 19 29
|
syl2anc |
|
31 |
23 24 2 28
|
iporthcom |
|
32 |
17 22 20 31
|
syl3anc |
|
33 |
30 32
|
mpbid |
|
34 |
33
|
oveq1d |
|
35 |
17 9
|
syl |
|
36 |
23
|
lmodfgrp |
|
37 |
35 36
|
syl |
|
38 |
|
eqid |
|
39 |
23 24 2 38
|
ipcl |
|
40 |
17 22 22 39
|
syl3anc |
|
41 |
38 25 28
|
grplid |
|
42 |
37 40 41
|
syl2anc |
|
43 |
27 34 42
|
3eqtrd |
|
44 |
|
simpr |
|
45 |
2 24 23 28 3
|
ocvi |
|
46 |
44 21 45
|
syl2anc |
|
47 |
43 46
|
eqtr3d |
|
48 |
|
eqid |
|
49 |
23 24 2 28 48
|
ipeq0 |
|
50 |
17 22 49
|
syl2anc |
|
51 |
47 50
|
mpbid |
|
52 |
51
|
oveq2d |
|
53 |
|
lmodgrp |
|
54 |
10 53
|
syl |
|
55 |
54
|
ad2antrr |
|
56 |
2 13 48
|
grprid |
|
57 |
55 20 56
|
syl2anc |
|
58 |
52 57
|
eqtrd |
|
59 |
58 19
|
eqeltrd |
|
60 |
59
|
ex |
|
61 |
|
eleq1 |
|
62 |
|
eleq1 |
|
63 |
61 62
|
imbi12d |
|
64 |
60 63
|
syl5ibrcom |
|
65 |
64
|
rexlimdvva |
|
66 |
16 65
|
syld |
|
67 |
66
|
pm2.43d |
|
68 |
67
|
ssrdv |
|
69 |
2 1 3
|
iscss2 |
|
70 |
5 6 69
|
syl2anc |
|
71 |
68 70
|
mpbird |
|