Step |
Hyp |
Ref |
Expression |
1 |
|
eqgvscpbl.v |
|
2 |
|
eqgvscpbl.e |
|
3 |
|
eqgvscpbl.s |
|
4 |
|
eqgvscpbl.p |
|
5 |
|
eqgvscpbl.m |
|
6 |
|
eqgvscpbl.g |
|
7 |
|
eqgvscpbl.k |
|
8 |
5
|
adantr |
|
9 |
7
|
adantr |
|
10 |
|
simpr1 |
|
11 |
|
eqid |
|
12 |
1 11 4 3
|
lmodvscl |
|
13 |
8 9 10 12
|
syl3anc |
|
14 |
|
simpr2 |
|
15 |
1 11 4 3
|
lmodvscl |
|
16 |
8 9 14 15
|
syl3anc |
|
17 |
5
|
ad2antrr |
|
18 |
7
|
ad2antrr |
|
19 |
|
lmodgrp |
|
20 |
17 19
|
syl |
|
21 |
|
simplr |
|
22 |
|
eqid |
|
23 |
1 22
|
grpinvcl |
|
24 |
20 21 23
|
syl2anc |
|
25 |
|
simpr |
|
26 |
|
eqid |
|
27 |
1 26 11 4 3
|
lmodvsdi |
|
28 |
17 18 24 25 27
|
syl13anc |
|
29 |
1 11 4 22 3
|
lmodvsinv2 |
|
30 |
17 18 21 29
|
syl3anc |
|
31 |
30
|
oveq1d |
|
32 |
28 31
|
eqtrd |
|
33 |
32
|
anasss |
|
34 |
33
|
3adantr3 |
|
35 |
6
|
adantr |
|
36 |
|
simpr3 |
|
37 |
|
eqid |
|
38 |
11 4 3 37
|
lssvscl |
|
39 |
8 35 9 36 38
|
syl22anc |
|
40 |
34 39
|
eqeltrrd |
|
41 |
13 16 40
|
3jca |
|
42 |
41
|
ex |
|
43 |
5 19
|
syl |
|
44 |
37
|
lsssubg |
|
45 |
5 6 44
|
syl2anc |
|
46 |
1
|
subgss |
|
47 |
45 46
|
syl |
|
48 |
1 22 26 2
|
eqgval |
|
49 |
43 47 48
|
syl2anc |
|
50 |
1 22 26 2
|
eqgval |
|
51 |
43 47 50
|
syl2anc |
|
52 |
42 49 51
|
3imtr4d |
|