Step |
Hyp |
Ref |
Expression |
1 |
|
rhmmpl.p |
|
2 |
|
rhmmpl.q |
|
3 |
|
rhmmpl.b |
|
4 |
|
rhmmpl.f |
|
5 |
|
rhmmpl.i |
|
6 |
|
rhmmpl.h |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
|
rhmrcl1 |
|
12 |
6 11
|
syl |
|
13 |
1 5 12
|
mplringd |
|
14 |
|
rhmrcl2 |
|
15 |
6 14
|
syl |
|
16 |
2 5 15
|
mplringd |
|
17 |
|
eqid |
|
18 |
|
eqid |
|
19 |
|
eqid |
|
20 |
1 17 18 19 7 5 12
|
mpl1 |
|
21 |
20
|
coeq2d |
|
22 |
|
eqid |
|
23 |
|
eqid |
|
24 |
22 23
|
rhmf |
|
25 |
6 24
|
syl |
|
26 |
22 19
|
ringidcl |
|
27 |
12 26
|
syl |
|
28 |
22 18
|
ring0cl |
|
29 |
12 28
|
syl |
|
30 |
27 29
|
ifcld |
|
31 |
30
|
adantr |
|
32 |
25 31
|
cofmpt |
|
33 |
|
fvif |
|
34 |
|
eqid |
|
35 |
19 34
|
rhm1 |
|
36 |
6 35
|
syl |
|
37 |
|
rhmghm |
|
38 |
|
eqid |
|
39 |
18 38
|
ghmid |
|
40 |
6 37 39
|
3syl |
|
41 |
36 40
|
ifeq12d |
|
42 |
33 41
|
eqtrid |
|
43 |
42
|
mpteq2dv |
|
44 |
21 32 43
|
3eqtrd |
|
45 |
|
coeq2 |
|
46 |
3 7
|
ringidcl |
|
47 |
13 46
|
syl |
|
48 |
6 47
|
coexd |
|
49 |
4 45 47 48
|
fvmptd3 |
|
50 |
2 17 38 34 8 5 15
|
mpl1 |
|
51 |
44 49 50
|
3eqtr4d |
|
52 |
|
eqid |
|
53 |
6
|
adantr |
|
54 |
|
simprl |
|
55 |
|
simprr |
|
56 |
1 2 3 52 9 10 53 54 55
|
rhmcomulmpl |
|
57 |
|
coeq2 |
|
58 |
13
|
adantr |
|
59 |
3 9 58 54 55
|
ringcld |
|
60 |
|
ovexd |
|
61 |
53 60
|
coexd |
|
62 |
4 57 59 61
|
fvmptd3 |
|
63 |
|
coeq2 |
|
64 |
53 54
|
coexd |
|
65 |
4 63 54 64
|
fvmptd3 |
|
66 |
|
coeq2 |
|
67 |
53 55
|
coexd |
|
68 |
4 66 55 67
|
fvmptd3 |
|
69 |
65 68
|
oveq12d |
|
70 |
56 62 69
|
3eqtr4d |
|
71 |
|
eqid |
|
72 |
|
eqid |
|
73 |
|
ghmmhm |
|
74 |
6 37 73
|
3syl |
|
75 |
74
|
adantr |
|
76 |
|
simpr |
|
77 |
1 2 3 52 75 76
|
mhmcompl |
|
78 |
77 4
|
fmptd |
|
79 |
53 37 73
|
3syl |
|
80 |
1 2 3 52 71 72 79 54 55
|
mhmcoaddmpl |
|
81 |
|
coeq2 |
|
82 |
13
|
ringgrpd |
|
83 |
82
|
adantr |
|
84 |
3 71 83 54 55
|
grpcld |
|
85 |
|
ovexd |
|
86 |
53 85
|
coexd |
|
87 |
4 81 84 86
|
fvmptd3 |
|
88 |
65 68
|
oveq12d |
|
89 |
80 87 88
|
3eqtr4d |
|
90 |
3 7 8 9 10 13 16 51 70 52 71 72 78 89
|
isrhmd |
|