Step |
Hyp |
Ref |
Expression |
1 |
|
mplind.sk |
|
2 |
|
mplind.sv |
|
3 |
|
mplind.sy |
|
4 |
|
mplind.sp |
|
5 |
|
mplind.st |
|
6 |
|
mplind.sc |
|
7 |
|
mplind.sb |
|
8 |
|
mplind.p |
|
9 |
|
mplind.t |
|
10 |
|
mplind.s |
|
11 |
|
mplind.v |
|
12 |
|
mplind.x |
|
13 |
|
mplind.i |
|
14 |
|
mplind.r |
|
15 |
|
eqid |
|
16 |
15 13 14
|
psrassa |
|
17 |
|
inss2 |
|
18 |
|
crngring |
|
19 |
14 18
|
syl |
|
20 |
15 3 7 13 19
|
mplsubrg |
|
21 |
|
eqid |
|
22 |
21
|
subrgss |
|
23 |
20 22
|
syl |
|
24 |
17 23
|
sstrid |
|
25 |
3 2 7 13 19
|
mvrf2 |
|
26 |
25
|
ffnd |
|
27 |
11
|
ralrimiva |
|
28 |
|
fnfvrnss |
|
29 |
26 27 28
|
syl2anc |
|
30 |
25
|
frnd |
|
31 |
29 30
|
ssind |
|
32 |
|
eqid |
|
33 |
32 21
|
aspss |
|
34 |
16 24 31 33
|
syl3anc |
|
35 |
3 15 2 32 13 14
|
mplbas2 |
|
36 |
35 7
|
eqtr4di |
|
37 |
17
|
a1i |
|
38 |
3
|
mplassa |
|
39 |
13 14 38
|
syl2anc |
|
40 |
|
eqid |
|
41 |
6 40
|
asclrhm |
|
42 |
39 41
|
syl |
|
43 |
|
eqid |
|
44 |
|
eqid |
|
45 |
43 44
|
rhm1 |
|
46 |
42 45
|
syl |
|
47 |
|
fveq2 |
|
48 |
47
|
eleq1d |
|
49 |
10
|
ralrimiva |
|
50 |
3 13 14
|
mplsca |
|
51 |
50 19
|
eqeltrrd |
|
52 |
|
eqid |
|
53 |
52 43
|
ringidcl |
|
54 |
51 53
|
syl |
|
55 |
50
|
fveq2d |
|
56 |
1 55
|
syl5eq |
|
57 |
54 56
|
eleqtrrd |
|
58 |
48 49 57
|
rspcdva |
|
59 |
46 58
|
eqeltrrd |
|
60 |
|
assaring |
|
61 |
39 60
|
syl |
|
62 |
7 44
|
ringidcl |
|
63 |
61 62
|
syl |
|
64 |
59 63
|
elind |
|
65 |
64
|
ne0d |
|
66 |
|
elinel1 |
|
67 |
|
elinel1 |
|
68 |
66 67
|
anim12i |
|
69 |
8
|
caovclg |
|
70 |
68 69
|
sylan2 |
|
71 |
|
assalmod |
|
72 |
39 71
|
syl |
|
73 |
|
lmodgrp |
|
74 |
72 73
|
syl |
|
75 |
74
|
adantr |
|
76 |
|
simprl |
|
77 |
76
|
elin2d |
|
78 |
|
simprr |
|
79 |
78
|
elin2d |
|
80 |
7 4
|
grpcl |
|
81 |
75 77 79 80
|
syl3anc |
|
82 |
70 81
|
elind |
|
83 |
82
|
anassrs |
|
84 |
83
|
ralrimiva |
|
85 |
|
eqid |
|
86 |
61
|
adantr |
|
87 |
|
simpr |
|
88 |
87
|
elin2d |
|
89 |
7 5 44 85 86 88
|
ringnegl |
|
90 |
|
simpl |
|
91 |
|
rhmghm |
|
92 |
42 91
|
syl |
|
93 |
|
eqid |
|
94 |
52 93 85
|
ghminv |
|
95 |
92 54 94
|
syl2anc |
|
96 |
46
|
fveq2d |
|
97 |
95 96
|
eqtrd |
|
98 |
|
fveq2 |
|
99 |
98
|
eleq1d |
|
100 |
|
ringgrp |
|
101 |
51 100
|
syl |
|
102 |
52 93
|
grpinvcl |
|
103 |
101 54 102
|
syl2anc |
|
104 |
103 56
|
eleqtrrd |
|
105 |
99 49 104
|
rspcdva |
|
106 |
97 105
|
eqeltrrd |
|
107 |
106
|
adantr |
|
108 |
87
|
elin1d |
|
109 |
9
|
caovclg |
|
110 |
90 107 108 109
|
syl12anc |
|
111 |
89 110
|
eqeltrrd |
|
112 |
74
|
adantr |
|
113 |
7 85
|
grpinvcl |
|
114 |
112 88 113
|
syl2anc |
|
115 |
111 114
|
elind |
|
116 |
84 115
|
jca |
|
117 |
116
|
ralrimiva |
|
118 |
7 4 85
|
issubg2 |
|
119 |
74 118
|
syl |
|
120 |
37 65 117 119
|
mpbir3and |
|
121 |
|
elinel1 |
|
122 |
|
elinel1 |
|
123 |
121 122
|
anim12i |
|
124 |
123 9
|
sylan2 |
|
125 |
61
|
adantr |
|
126 |
|
simprl |
|
127 |
126
|
elin2d |
|
128 |
|
simprr |
|
129 |
128
|
elin2d |
|
130 |
7 5
|
ringcl |
|
131 |
125 127 129 130
|
syl3anc |
|
132 |
124 131
|
elind |
|
133 |
132
|
ralrimivva |
|
134 |
7 44 5
|
issubrg2 |
|
135 |
61 134
|
syl |
|
136 |
120 64 133 135
|
mpbir3and |
|
137 |
3 15 7
|
mplval2 |
|
138 |
137
|
subsubrg |
|
139 |
138
|
simprbda |
|
140 |
20 136 139
|
syl2anc |
|
141 |
|
assalmod |
|
142 |
16 141
|
syl |
|
143 |
15 3 7 13 19
|
mpllss |
|
144 |
39
|
adantr |
|
145 |
|
simprl |
|
146 |
|
simprr |
|
147 |
146
|
elin2d |
|
148 |
|
eqid |
|
149 |
6 40 52 7 5 148
|
asclmul1 |
|
150 |
144 145 147 149
|
syl3anc |
|
151 |
|
fveq2 |
|
152 |
151
|
eleq1d |
|
153 |
49
|
adantr |
|
154 |
56
|
adantr |
|
155 |
145 154
|
eleqtrrd |
|
156 |
152 153 155
|
rspcdva |
|
157 |
146
|
elin1d |
|
158 |
156 157
|
jca |
|
159 |
9
|
caovclg |
|
160 |
158 159
|
syldan |
|
161 |
150 160
|
eqeltrrd |
|
162 |
72
|
adantr |
|
163 |
7 40 148 52
|
lmodvscl |
|
164 |
162 145 147 163
|
syl3anc |
|
165 |
161 164
|
elind |
|
166 |
165
|
ralrimivva |
|
167 |
|
eqid |
|
168 |
40 52 7 148 167
|
islss4 |
|
169 |
72 168
|
syl |
|
170 |
120 166 169
|
mpbir2and |
|
171 |
|
eqid |
|
172 |
137 171 167
|
lsslss |
|
173 |
172
|
simprbda |
|
174 |
142 143 170 173
|
syl21anc |
|
175 |
32 21 171
|
aspid |
|
176 |
16 140 174 175
|
syl3anc |
|
177 |
34 36 176
|
3sstr3d |
|
178 |
177 12
|
sseldd |
|
179 |
178
|
elin1d |
|