Step |
Hyp |
Ref |
Expression |
1 |
|
eqid |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
|
eqid |
|
5 |
|
eqid |
|
6 |
|
rhmrcl1 |
|
7 |
|
eqid |
|
8 |
7
|
opprringb |
|
9 |
6 8
|
sylib |
|
10 |
|
rhmrcl2 |
|
11 |
|
eqid |
|
12 |
11
|
opprringb |
|
13 |
10 12
|
sylib |
|
14 |
|
eqid |
|
15 |
7 14
|
oppr1 |
|
16 |
15
|
eqcomi |
|
17 |
|
eqid |
|
18 |
11 17
|
oppr1 |
|
19 |
18
|
eqcomi |
|
20 |
16 19
|
rhm1 |
|
21 |
|
simpl |
|
22 |
|
simprr |
|
23 |
|
eqid |
|
24 |
7 23
|
opprbas |
|
25 |
22 24
|
eleqtrrdi |
|
26 |
|
simprl |
|
27 |
26 24
|
eleqtrrdi |
|
28 |
|
eqid |
|
29 |
|
eqid |
|
30 |
23 28 29
|
rhmmul |
|
31 |
21 25 27 30
|
syl3anc |
|
32 |
23 28 7 4
|
opprmul |
|
33 |
32
|
fveq2i |
|
34 |
|
eqid |
|
35 |
34 29 11 5
|
opprmul |
|
36 |
31 33 35
|
3eqtr4g |
|
37 |
|
ringgrp |
|
38 |
9 37
|
syl |
|
39 |
|
ringgrp |
|
40 |
13 39
|
syl |
|
41 |
23 34
|
rhmf |
|
42 |
|
rhmghm |
|
43 |
42
|
ad2antrr |
|
44 |
|
simplr |
|
45 |
|
simpr |
|
46 |
|
eqid |
|
47 |
|
eqid |
|
48 |
23 46 47
|
ghmlin |
|
49 |
43 44 45 48
|
syl3anc |
|
50 |
49
|
ralrimiva |
|
51 |
50
|
ralrimiva |
|
52 |
41 51
|
jca |
|
53 |
38 40 52
|
jca31 |
|
54 |
11 34
|
opprbas |
|
55 |
7 46
|
oppradd |
|
56 |
11 47
|
oppradd |
|
57 |
24 54 55 56
|
isghm |
|
58 |
53 57
|
sylibr |
|
59 |
1 2 3 4 5 9 13 20 36 58
|
isrhm2d |
|