Step |
Hyp |
Ref |
Expression |
1 |
|
lspsnneg.v |
|
2 |
|
lspsnneg.m |
|
3 |
|
lspsnneg.n |
|
4 |
|
eqid |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
1 2 4 5 6 7
|
lmodvneg1 |
|
9 |
8
|
sneqd |
|
10 |
9
|
fveq2d |
|
11 |
|
simpl |
|
12 |
4
|
lmodfgrp |
|
13 |
|
eqid |
|
14 |
4 13 6
|
lmod1cl |
|
15 |
13 7
|
grpinvcl |
|
16 |
12 14 15
|
syl2anc |
|
17 |
16
|
adantr |
|
18 |
|
simpr |
|
19 |
4 13 1 5 3
|
lspsnvsi |
|
20 |
11 17 18 19
|
syl3anc |
|
21 |
10 20
|
eqsstrrd |
|
22 |
1 2
|
lmodvnegcl |
|
23 |
1 2 4 5 6 7
|
lmodvneg1 |
|
24 |
22 23
|
syldan |
|
25 |
|
lmodgrp |
|
26 |
1 2
|
grpinvinv |
|
27 |
25 26
|
sylan |
|
28 |
24 27
|
eqtrd |
|
29 |
28
|
sneqd |
|
30 |
29
|
fveq2d |
|
31 |
4 13 1 5 3
|
lspsnvsi |
|
32 |
11 17 22 31
|
syl3anc |
|
33 |
30 32
|
eqsstrrd |
|
34 |
21 33
|
eqssd |
|