Step |
Hyp |
Ref |
Expression |
1 |
|
ringlz.1 |
|
2 |
|
ringlz.2 |
|
3 |
|
ringlz.3 |
|
4 |
|
ringlz.4 |
|
5 |
3
|
rngogrpo |
|
6 |
2 1
|
grpoidcl |
|
7 |
2 1
|
grpolid |
|
8 |
5 6 7
|
syl2anc2 |
|
9 |
8
|
adantr |
|
10 |
9
|
oveq1d |
|
11 |
3 2 1
|
rngo0cl |
|
12 |
11
|
adantr |
|
13 |
|
simpr |
|
14 |
12 12 13
|
3jca |
|
15 |
3 4 2
|
rngodir |
|
16 |
14 15
|
syldan |
|
17 |
5
|
adantr |
|
18 |
|
simpl |
|
19 |
3 4 2
|
rngocl |
|
20 |
18 12 13 19
|
syl3anc |
|
21 |
2 1
|
grporid |
|
22 |
21
|
eqcomd |
|
23 |
17 20 22
|
syl2anc |
|
24 |
10 16 23
|
3eqtr3d |
|
25 |
2
|
grpolcan |
|
26 |
17 20 12 20 25
|
syl13anc |
|
27 |
24 26
|
mpbid |
|