Step |
Hyp |
Ref |
Expression |
1 |
|
mulgmhm.b |
|
2 |
|
mulgmhm.m |
|
3 |
|
eqid |
|
4 |
|
ablgrp |
|
5 |
4
|
adantr |
|
6 |
1 2
|
mulgcl |
|
7 |
4 6
|
syl3an1 |
|
8 |
7
|
3expa |
|
9 |
8
|
fmpttd |
|
10 |
|
3anass |
|
11 |
1 2 3
|
mulgdi |
|
12 |
10 11
|
sylan2br |
|
13 |
12
|
anassrs |
|
14 |
1 3
|
grpcl |
|
15 |
14
|
3expb |
|
16 |
5 15
|
sylan |
|
17 |
|
oveq2 |
|
18 |
|
eqid |
|
19 |
|
ovex |
|
20 |
17 18 19
|
fvmpt |
|
21 |
16 20
|
syl |
|
22 |
|
oveq2 |
|
23 |
|
ovex |
|
24 |
22 18 23
|
fvmpt |
|
25 |
|
oveq2 |
|
26 |
|
ovex |
|
27 |
25 18 26
|
fvmpt |
|
28 |
24 27
|
oveqan12d |
|
29 |
28
|
adantl |
|
30 |
13 21 29
|
3eqtr4d |
|
31 |
1 1 3 3 5 5 9 30
|
isghmd |
|