Step |
Hyp |
Ref |
Expression |
1 |
|
galcan.1 |
|
2 |
|
oveq2 |
|
3 |
|
simpl |
|
4 |
|
gagrp |
|
5 |
3 4
|
syl |
|
6 |
|
simpr1 |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
|
eqid |
|
10 |
1 7 8 9
|
grplinv |
|
11 |
5 6 10
|
syl2anc |
|
12 |
11
|
oveq1d |
|
13 |
1 9
|
grpinvcl |
|
14 |
5 6 13
|
syl2anc |
|
15 |
|
simpr2 |
|
16 |
1 7
|
gaass |
|
17 |
3 14 6 15 16
|
syl13anc |
|
18 |
8
|
gagrpid |
|
19 |
3 15 18
|
syl2anc |
|
20 |
12 17 19
|
3eqtr3d |
|
21 |
11
|
oveq1d |
|
22 |
|
simpr3 |
|
23 |
1 7
|
gaass |
|
24 |
3 14 6 22 23
|
syl13anc |
|
25 |
8
|
gagrpid |
|
26 |
3 22 25
|
syl2anc |
|
27 |
21 24 26
|
3eqtr3d |
|
28 |
20 27
|
eqeq12d |
|
29 |
2 28
|
syl5ib |
|
30 |
|
oveq2 |
|
31 |
29 30
|
impbid1 |
|