Step |
Hyp |
Ref |
Expression |
1 |
|
grplmulf1o.b |
|
2 |
|
grplmulf1o.p |
|
3 |
|
grplmulf1o.n |
|
4 |
1 2
|
grpcl |
|
5 |
4
|
3expa |
|
6 |
|
eqid |
|
7 |
1 6
|
grpinvcl |
|
8 |
1 2
|
grpcl |
|
9 |
8
|
3expa |
|
10 |
7 9
|
syldanl |
|
11 |
|
eqcom |
|
12 |
|
simpll |
|
13 |
10
|
adantrl |
|
14 |
|
simprl |
|
15 |
|
simplr |
|
16 |
1 2
|
grplcan |
|
17 |
12 13 14 15 16
|
syl13anc |
|
18 |
|
eqid |
|
19 |
1 2 18 6
|
grprinv |
|
20 |
19
|
adantr |
|
21 |
20
|
oveq1d |
|
22 |
7
|
adantr |
|
23 |
|
simprr |
|
24 |
1 2
|
grpass |
|
25 |
12 15 22 23 24
|
syl13anc |
|
26 |
1 2 18
|
grplid |
|
27 |
26
|
ad2ant2rl |
|
28 |
21 25 27
|
3eqtr3d |
|
29 |
28
|
eqeq1d |
|
30 |
17 29
|
bitr3d |
|
31 |
11 30
|
syl5bb |
|
32 |
3 5 10 31
|
f1o2d |
|