Step |
Hyp |
Ref |
Expression |
1 |
|
lspabs2.v |
|
2 |
|
lspabs2.p |
|
3 |
|
lspabs2.o |
|
4 |
|
lspabs2.n |
|
5 |
|
lspabs2.w |
|
6 |
|
lspabs2.x |
|
7 |
|
lspabs2.y |
|
8 |
|
lspabs2.e |
|
9 |
|
lveclmod |
|
10 |
5 9
|
syl |
|
11 |
1 4
|
lspsnsubg |
|
12 |
10 6 11
|
syl2anc |
|
13 |
7
|
eldifad |
|
14 |
1 4
|
lspsnsubg |
|
15 |
10 13 14
|
syl2anc |
|
16 |
|
eqid |
|
17 |
16
|
lsmub2 |
|
18 |
12 15 17
|
syl2anc |
|
19 |
8
|
oveq2d |
|
20 |
16
|
lsmidm |
|
21 |
12 20
|
syl |
|
22 |
1 2 4 10 6 13
|
lspprabs |
|
23 |
1 2
|
lmodvacl |
|
24 |
10 6 13 23
|
syl3anc |
|
25 |
1 4 16 10 6 24
|
lsmpr |
|
26 |
1 4 16 10 6 13
|
lsmpr |
|
27 |
22 25 26
|
3eqtr3d |
|
28 |
19 21 27
|
3eqtr3rd |
|
29 |
18 28
|
sseqtrd |
|
30 |
1 3 4 5 7 6
|
lspsncmp |
|
31 |
29 30
|
mpbid |
|
32 |
31
|
eqcomd |
|