Step |
Hyp |
Ref |
Expression |
1 |
|
grpsubpropd2.1 |
|
2 |
|
grpsubpropd2.2 |
|
3 |
|
grpsubpropd2.3 |
|
4 |
|
grpsubpropd2.4 |
|
5 |
|
simp1 |
|
6 |
|
simp2 |
|
7 |
1
|
3ad2ant1 |
|
8 |
6 7
|
eleqtrrd |
|
9 |
3
|
3ad2ant1 |
|
10 |
|
simp3 |
|
11 |
|
eqid |
|
12 |
|
eqid |
|
13 |
11 12
|
grpinvcl |
|
14 |
9 10 13
|
syl2anc |
|
15 |
14 7
|
eleqtrrd |
|
16 |
4
|
oveqrspc2v |
|
17 |
5 8 15 16
|
syl12anc |
|
18 |
1 2 4
|
grpinvpropd |
|
19 |
18
|
fveq1d |
|
20 |
19
|
oveq2d |
|
21 |
20
|
3ad2ant1 |
|
22 |
17 21
|
eqtrd |
|
23 |
22
|
mpoeq3dva |
|
24 |
1 2
|
eqtr3d |
|
25 |
|
mpoeq12 |
|
26 |
24 24 25
|
syl2anc |
|
27 |
23 26
|
eqtrd |
|
28 |
|
eqid |
|
29 |
|
eqid |
|
30 |
11 28 12 29
|
grpsubfval |
|
31 |
|
eqid |
|
32 |
|
eqid |
|
33 |
|
eqid |
|
34 |
|
eqid |
|
35 |
31 32 33 34
|
grpsubfval |
|
36 |
27 30 35
|
3eqtr4g |
|