Step |
Hyp |
Ref |
Expression |
1 |
|
simpl |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
2 3
|
unitss |
|
5 |
|
simpr |
|
6 |
4 5
|
sselid |
|
7 |
|
rhmrcl1 |
|
8 |
|
eqid |
|
9 |
2 8
|
ringidcl |
|
10 |
1 7 9
|
3syl |
|
11 |
|
eqid |
|
12 |
|
eqid |
|
13 |
|
eqid |
|
14 |
3 8 11 12 13
|
isunit |
|
15 |
5 14
|
sylib |
|
16 |
15
|
simpld |
|
17 |
|
eqid |
|
18 |
2 11 17
|
rhmdvdsr |
|
19 |
1 6 10 16 18
|
syl31anc |
|
20 |
|
eqid |
|
21 |
8 20
|
rhm1 |
|
22 |
21
|
breq2d |
|
23 |
22
|
adantr |
|
24 |
19 23
|
mpbid |
|
25 |
|
rhmopp |
|
26 |
25
|
adantr |
|
27 |
15
|
simprd |
|
28 |
12 2
|
opprbas |
|
29 |
|
eqid |
|
30 |
28 13 29
|
rhmdvdsr |
|
31 |
26 6 10 27 30
|
syl31anc |
|
32 |
21
|
breq2d |
|
33 |
32
|
adantr |
|
34 |
31 33
|
mpbid |
|
35 |
|
eqid |
|
36 |
|
eqid |
|
37 |
35 20 17 36 29
|
isunit |
|
38 |
24 34 37
|
sylanbrc |
|