Step |
Hyp |
Ref |
Expression |
1 |
|
frobrhm.1 |
|
2 |
|
frobrhm.2 |
|
3 |
|
frobrhm.3 |
|
4 |
|
frobrhm.4 |
|
5 |
|
frobrhm.5 |
|
6 |
|
frobrhm.6 |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
5
|
crngringd |
|
10 |
|
simpr |
|
11 |
10
|
oveq2d |
|
12 |
|
eqid |
|
13 |
12
|
ringmgp |
|
14 |
9 13
|
syl |
|
15 |
|
prmnn |
|
16 |
|
nnnn0 |
|
17 |
6 15 16
|
3syl |
|
18 |
12 1
|
mgpbas |
|
19 |
12 7
|
ringidval |
|
20 |
18 3 19
|
mulgnn0z |
|
21 |
14 17 20
|
syl2anc |
|
22 |
21
|
adantr |
|
23 |
11 22
|
eqtrd |
|
24 |
1 7
|
ringidcl |
|
25 |
9 24
|
syl |
|
26 |
4 23 25 25
|
fvmptd2 |
|
27 |
12
|
crngmgp |
|
28 |
5 27
|
syl |
|
29 |
28
|
adantr |
|
30 |
17
|
adantr |
|
31 |
|
simprl |
|
32 |
|
simprr |
|
33 |
12 8
|
mgpplusg |
|
34 |
18 3 33
|
mulgnn0di |
|
35 |
29 30 31 32 34
|
syl13anc |
|
36 |
|
simpr |
|
37 |
36
|
oveq2d |
|
38 |
9
|
adantr |
|
39 |
1 8
|
ringcl |
|
40 |
38 31 32 39
|
syl3anc |
|
41 |
|
ovexd |
|
42 |
4 37 40 41
|
fvmptd2 |
|
43 |
|
simpr |
|
44 |
43
|
oveq2d |
|
45 |
|
ovexd |
|
46 |
4 44 31 45
|
fvmptd2 |
|
47 |
|
simpr |
|
48 |
47
|
oveq2d |
|
49 |
|
ovexd |
|
50 |
4 48 32 49
|
fvmptd2 |
|
51 |
46 50
|
oveq12d |
|
52 |
35 42 51
|
3eqtr4d |
|
53 |
|
eqid |
|
54 |
14
|
adantr |
|
55 |
17
|
adantr |
|
56 |
|
simpr |
|
57 |
18 3
|
mulgnn0cl |
|
58 |
54 55 56 57
|
syl3anc |
|
59 |
58 4
|
fmptd |
|
60 |
5
|
adantr |
|
61 |
6
|
adantr |
|
62 |
1 53 3 2 60 61 31 32
|
freshmansdream |
|
63 |
|
simpr |
|
64 |
63
|
oveq2d |
|
65 |
1 53
|
ringacl |
|
66 |
38 31 32 65
|
syl3anc |
|
67 |
|
ovexd |
|
68 |
4 64 66 67
|
fvmptd2 |
|
69 |
46 50
|
oveq12d |
|
70 |
62 68 69
|
3eqtr4d |
|
71 |
1 7 7 8 8 9 9 26 52 1 53 53 59 70
|
isrhmd |
|