Step |
Hyp |
Ref |
Expression |
1 |
|
ogrpinvlt.0 |
|
2 |
|
ogrpinvlt.1 |
|
3 |
|
ogrpinvlt.2 |
|
4 |
|
simp1l |
|
5 |
|
simp2 |
|
6 |
|
simp3 |
|
7 |
|
ogrpgrp |
|
8 |
4 7
|
syl |
|
9 |
1 3
|
grpinvcl |
|
10 |
8 6 9
|
syl2anc |
|
11 |
|
eqid |
|
12 |
1 2 11
|
ogrpaddltbi |
|
13 |
4 5 6 10 12
|
syl13anc |
|
14 |
|
eqid |
|
15 |
1 11 14 3
|
grprinv |
|
16 |
8 6 15
|
syl2anc |
|
17 |
16
|
breq2d |
|
18 |
|
simp1r |
|
19 |
1 11
|
grpcl |
|
20 |
8 5 10 19
|
syl3anc |
|
21 |
1 14
|
grpidcl |
|
22 |
4 7 21
|
3syl |
|
23 |
1 3
|
grpinvcl |
|
24 |
8 5 23
|
syl2anc |
|
25 |
1 2 11 4 18 20 22 24
|
ogrpaddltrbid |
|
26 |
13 17 25
|
3bitrd |
|
27 |
1 11 14 3
|
grplinv |
|
28 |
8 5 27
|
syl2anc |
|
29 |
28
|
oveq1d |
|
30 |
1 11
|
grpass |
|
31 |
8 24 5 10 30
|
syl13anc |
|
32 |
1 11 14
|
grplid |
|
33 |
8 10 32
|
syl2anc |
|
34 |
29 31 33
|
3eqtr3d |
|
35 |
1 11 14
|
grprid |
|
36 |
8 24 35
|
syl2anc |
|
37 |
34 36
|
breq12d |
|
38 |
26 37
|
bitrd |
|