| Step |
Hyp |
Ref |
Expression |
| 1 |
|
zrhcntr.1 |
|
| 2 |
|
zrhcntr.2 |
|
| 3 |
|
zrhcntr.3 |
|
| 4 |
|
zrhcntr.4 |
|
| 5 |
|
zrhcntr.5 |
|
| 6 |
|
fveq2 |
|
| 7 |
6
|
eleq1d |
|
| 8 |
|
fveq2 |
|
| 9 |
8
|
eleq1d |
|
| 10 |
|
fveq2 |
|
| 11 |
10
|
eleq1d |
|
| 12 |
|
fveq2 |
|
| 13 |
12
|
eleq1d |
|
| 14 |
|
fveq2 |
|
| 15 |
14
|
eleq1d |
|
| 16 |
|
eqid |
|
| 17 |
3 16
|
zrh0 |
|
| 18 |
4 17
|
syl |
|
| 19 |
|
eqid |
|
| 20 |
19 16
|
ring0cl |
|
| 21 |
4 20
|
syl |
|
| 22 |
18 21
|
eqeltrd |
|
| 23 |
|
eqid |
|
| 24 |
4
|
adantr |
|
| 25 |
|
simpr |
|
| 26 |
19 23 16 24 25
|
ringlzd |
|
| 27 |
19 23 16 24 25
|
ringrzd |
|
| 28 |
26 27
|
eqtr4d |
|
| 29 |
18
|
oveq1d |
|
| 30 |
29
|
adantr |
|
| 31 |
18
|
oveq2d |
|
| 32 |
31
|
adantr |
|
| 33 |
28 30 32
|
3eqtr4d |
|
| 34 |
33
|
ralrimiva |
|
| 35 |
1 19
|
mgpbas |
|
| 36 |
1 23
|
mgpplusg |
|
| 37 |
35 36 2
|
elcntr |
|
| 38 |
22 34 37
|
sylanbrc |
|
| 39 |
3
|
zrhrhm |
|
| 40 |
|
rhmghm |
|
| 41 |
4 39 40
|
3syl |
|
| 42 |
41
|
ad2antrr |
|
| 43 |
|
simplr |
|
| 44 |
43
|
nn0zd |
|
| 45 |
|
1zzd |
|
| 46 |
|
zringbas |
|
| 47 |
|
zringplusg |
|
| 48 |
|
eqid |
|
| 49 |
46 47 48
|
ghmlin |
|
| 50 |
42 44 45 49
|
syl3anc |
|
| 51 |
|
eqid |
|
| 52 |
3 51
|
zrh1 |
|
| 53 |
4 52
|
syl |
|
| 54 |
53
|
ad2antrr |
|
| 55 |
54
|
oveq2d |
|
| 56 |
50 55
|
eqtrd |
|
| 57 |
4
|
ringgrpd |
|
| 58 |
57
|
ad2antrr |
|
| 59 |
35
|
cntrss |
|
| 60 |
2 59
|
eqsstri |
|
| 61 |
60
|
a1i |
|
| 62 |
61
|
sselda |
|
| 63 |
19 51
|
ringidcl |
|
| 64 |
4 63
|
syl |
|
| 65 |
64
|
ad2antrr |
|
| 66 |
19 48 58 62 65
|
grpcld |
|
| 67 |
35 36 2
|
cntri |
|
| 68 |
67
|
adantll |
|
| 69 |
4
|
ad3antrrr |
|
| 70 |
|
simpr |
|
| 71 |
19 23 51 69 70
|
ringlidmd |
|
| 72 |
19 23 51 69 70
|
ringridmd |
|
| 73 |
71 72
|
eqtr4d |
|
| 74 |
68 73
|
oveq12d |
|
| 75 |
62
|
adantr |
|
| 76 |
69 63
|
syl |
|
| 77 |
19 48 23 69 75 76 70
|
ringdird |
|
| 78 |
19 48 23 69 70 75 76
|
ringdid |
|
| 79 |
74 77 78
|
3eqtr4d |
|
| 80 |
79
|
ralrimiva |
|
| 81 |
35 36 2
|
elcntr |
|
| 82 |
66 80 81
|
sylanbrc |
|
| 83 |
56 82
|
eqeltrd |
|
| 84 |
9 11 13 15 38 83
|
nn0indd |
|
| 85 |
84
|
ralrimiva |
|
| 86 |
85
|
adantr |
|
| 87 |
|
simpr |
|
| 88 |
7 86 87
|
rspcdva |
|
| 89 |
46 19
|
rhmf |
|
| 90 |
4 39 89
|
3syl |
|
| 91 |
90
|
adantr |
|
| 92 |
5
|
adantr |
|
| 93 |
91 92
|
ffvelcdmd |
|
| 94 |
|
eqid |
|
| 95 |
4
|
ad2antrr |
|
| 96 |
|
fveq2 |
|
| 97 |
96
|
eleq1d |
|
| 98 |
85
|
adantr |
|
| 99 |
|
simpr |
|
| 100 |
97 98 99
|
rspcdva |
|
| 101 |
35 36 2
|
elcntr |
|
| 102 |
100 101
|
sylib |
|
| 103 |
102
|
simpld |
|
| 104 |
103
|
adantr |
|
| 105 |
|
simpr |
|
| 106 |
19 23 94 95 104 105
|
ringmneg1 |
|
| 107 |
5
|
zcnd |
|
| 108 |
107
|
ad2antrr |
|
| 109 |
108
|
negnegd |
|
| 110 |
5
|
znegcld |
|
| 111 |
|
zringinvg |
|
| 112 |
110 111
|
syl |
|
| 113 |
112
|
ad2antrr |
|
| 114 |
109 113
|
eqtr3d |
|
| 115 |
114
|
fveq2d |
|
| 116 |
95 39 40
|
3syl |
|
| 117 |
110
|
ad2antrr |
|
| 118 |
|
eqid |
|
| 119 |
46 118 94
|
ghminv |
|
| 120 |
116 117 119
|
syl2anc |
|
| 121 |
115 120
|
eqtrd |
|
| 122 |
121
|
oveq1d |
|
| 123 |
19 23 94 95 105 104
|
ringmneg2 |
|
| 124 |
121
|
oveq2d |
|
| 125 |
102
|
simprd |
|
| 126 |
125
|
r19.21bi |
|
| 127 |
126
|
fveq2d |
|
| 128 |
123 124 127
|
3eqtr4d |
|
| 129 |
106 122 128
|
3eqtr4d |
|
| 130 |
129
|
ralrimiva |
|
| 131 |
35 36 2
|
elcntr |
|
| 132 |
93 130 131
|
sylanbrc |
|
| 133 |
|
elznn0 |
|
| 134 |
5 133
|
sylib |
|
| 135 |
134
|
simprd |
|
| 136 |
88 132 135
|
mpjaodan |
|