Step |
Hyp |
Ref |
Expression |
1 |
|
invghm.b |
|
2 |
|
invghm.m |
|
3 |
|
eqid |
|
4 |
|
ablgrp |
|
5 |
1 2
|
grpinvf |
|
6 |
4 5
|
syl |
|
7 |
1 3 2
|
ablinvadd |
|
8 |
7
|
3expb |
|
9 |
1 1 3 3 4 4 6 8
|
isghmd |
|
10 |
|
ghmgrp1 |
|
11 |
10
|
adantr |
|
12 |
|
simprr |
|
13 |
|
simprl |
|
14 |
1 3 2
|
grpinvadd |
|
15 |
11 12 13 14
|
syl3anc |
|
16 |
15
|
fveq2d |
|
17 |
|
simpl |
|
18 |
1 2
|
grpinvcl |
|
19 |
11 13 18
|
syl2anc |
|
20 |
1 2
|
grpinvcl |
|
21 |
11 12 20
|
syl2anc |
|
22 |
1 3 3
|
ghmlin |
|
23 |
17 19 21 22
|
syl3anc |
|
24 |
1 2
|
grpinvinv |
|
25 |
11 13 24
|
syl2anc |
|
26 |
1 2
|
grpinvinv |
|
27 |
11 12 26
|
syl2anc |
|
28 |
25 27
|
oveq12d |
|
29 |
16 23 28
|
3eqtrd |
|
30 |
1 3
|
grpcl |
|
31 |
11 12 13 30
|
syl3anc |
|
32 |
1 2
|
grpinvinv |
|
33 |
11 31 32
|
syl2anc |
|
34 |
29 33
|
eqtr3d |
|
35 |
34
|
ralrimivva |
|
36 |
1 3
|
isabl2 |
|
37 |
10 35 36
|
sylanbrc |
|
38 |
9 37
|
impbii |
|