Step |
Hyp |
Ref |
Expression |
1 |
|
mdetralt.d |
|
2 |
|
mdetralt.a |
|
3 |
|
mdetralt.b |
|
4 |
|
mdetralt.z |
|
5 |
|
mdetralt.r |
|
6 |
|
mdetralt.x |
|
7 |
|
mdetralt.i |
|
8 |
|
mdetralt.j |
|
9 |
|
mdetralt.ij |
|
10 |
|
mdetralt.eq |
|
11 |
|
eqid |
|
12 |
|
eqid |
|
13 |
|
eqid |
|
14 |
|
eqid |
|
15 |
|
eqid |
|
16 |
1 2 3 11 12 13 14 15
|
mdetleib |
|
17 |
6 16
|
syl |
|
18 |
|
eqid |
|
19 |
|
eqid |
|
20 |
|
crngring |
|
21 |
5 20
|
syl |
|
22 |
|
ringcmn |
|
23 |
21 22
|
syl |
|
24 |
2 3
|
matrcl |
|
25 |
6 24
|
syl |
|
26 |
25
|
simpld |
|
27 |
|
eqid |
|
28 |
27 11
|
symgbasfi |
|
29 |
26 28
|
syl |
|
30 |
21
|
adantr |
|
31 |
|
zrhpsgnmhm |
|
32 |
21 26 31
|
syl2anc |
|
33 |
15 18
|
mgpbas |
|
34 |
11 33
|
mhmf |
|
35 |
32 34
|
syl |
|
36 |
35
|
ffvelrnda |
|
37 |
15
|
crngmgp |
|
38 |
5 37
|
syl |
|
39 |
38
|
adantr |
|
40 |
26
|
adantr |
|
41 |
2 18 3
|
matbas2i |
|
42 |
6 41
|
syl |
|
43 |
|
elmapi |
|
44 |
42 43
|
syl |
|
45 |
44
|
ad2antrr |
|
46 |
27 11
|
symgbasf1o |
|
47 |
46
|
adantl |
|
48 |
|
f1of |
|
49 |
47 48
|
syl |
|
50 |
49
|
ffvelrnda |
|
51 |
|
simpr |
|
52 |
45 50 51
|
fovrnd |
|
53 |
52
|
ralrimiva |
|
54 |
33 39 40 53
|
gsummptcl |
|
55 |
18 14
|
ringcl |
|
56 |
30 36 54 55
|
syl3anc |
|
57 |
|
disjdif |
|
58 |
57
|
a1i |
|
59 |
27 11
|
evpmss |
|
60 |
|
undif |
|
61 |
59 60
|
mpbi |
|
62 |
61
|
eqcomi |
|
63 |
62
|
a1i |
|
64 |
|
eqid |
|
65 |
18 19 23 29 56 58 63 64
|
gsummptfidmsplitres |
|
66 |
|
resmpt |
|
67 |
59 66
|
ax-mp |
|
68 |
21
|
adantr |
|
69 |
26
|
adantr |
|
70 |
|
simpr |
|
71 |
|
eqid |
|
72 |
12 13 71
|
zrhpsgnevpm |
|
73 |
68 69 70 72
|
syl3anc |
|
74 |
73
|
oveq1d |
|
75 |
59
|
sseli |
|
76 |
75 54
|
sylan2 |
|
77 |
18 14 71
|
ringlidm |
|
78 |
68 76 77
|
syl2anc |
|
79 |
74 78
|
eqtrd |
|
80 |
79
|
mpteq2dva |
|
81 |
67 80
|
syl5eq |
|
82 |
81
|
oveq2d |
|
83 |
|
difss |
|
84 |
|
resmpt |
|
85 |
83 84
|
ax-mp |
|
86 |
21
|
adantr |
|
87 |
26
|
adantr |
|
88 |
|
simpr |
|
89 |
|
eqid |
|
90 |
12 13 71 11 89
|
zrhpsgnodpm |
|
91 |
86 87 88 90
|
syl3anc |
|
92 |
91
|
oveq1d |
|
93 |
|
eldifi |
|
94 |
93 54
|
sylan2 |
|
95 |
18 14 71 89 86 94
|
ringnegl |
|
96 |
92 95
|
eqtrd |
|
97 |
96
|
mpteq2dva |
|
98 |
|
ringgrp |
|
99 |
21 98
|
syl |
|
100 |
18 89
|
grpinvf |
|
101 |
99 100
|
syl |
|
102 |
101 94
|
cofmpt |
|
103 |
97 102
|
eqtr4d |
|
104 |
85 103
|
syl5eq |
|
105 |
104
|
oveq2d |
|
106 |
|
ringabl |
|
107 |
21 106
|
syl |
|
108 |
|
difssd |
|
109 |
29 108
|
ssfid |
|
110 |
|
eqid |
|
111 |
18 4 89 107 109 94 110
|
gsummptfidminv |
|
112 |
94
|
ralrimiva |
|
113 |
7 8
|
prssd |
|
114 |
|
pr2nelem |
|
115 |
7 8 9 114
|
syl3anc |
|
116 |
|
eqid |
|
117 |
|
eqid |
|
118 |
116 117
|
pmtrrn |
|
119 |
26 113 115 118
|
syl3anc |
|
120 |
27 11 117
|
pmtrodpm |
|
121 |
26 119 120
|
syl2anc |
|
122 |
27 11
|
evpmodpmf1o |
|
123 |
26 121 122
|
syl2anc |
|
124 |
18 23 109 112 110 123
|
gsummptfif1o |
|
125 |
|
eleq1w |
|
126 |
125
|
anbi2d |
|
127 |
|
oveq2 |
|
128 |
127
|
eleq1d |
|
129 |
126 128
|
imbi12d |
|
130 |
27
|
symggrp |
|
131 |
26 130
|
syl |
|
132 |
131
|
adantr |
|
133 |
117 27 11
|
symgtrf |
|
134 |
119
|
adantr |
|
135 |
133 134
|
sseldi |
|
136 |
75
|
adantl |
|
137 |
|
eqid |
|
138 |
11 137
|
grpcl |
|
139 |
132 135 136 138
|
syl3anc |
|
140 |
|
eqid |
|
141 |
27 13 140
|
psgnghm2 |
|
142 |
26 141
|
syl |
|
143 |
142
|
adantr |
|
144 |
|
prex |
|
145 |
|
eqid |
|
146 |
|
cnfldmul |
|
147 |
145 146
|
mgpplusg |
|
148 |
140 147
|
ressplusg |
|
149 |
144 148
|
ax-mp |
|
150 |
11 137 149
|
ghmlin |
|
151 |
143 135 136 150
|
syl3anc |
|
152 |
27 117 13
|
psgnpmtr |
|
153 |
134 152
|
syl |
|
154 |
27 11 13
|
psgnevpm |
|
155 |
26 154
|
sylan |
|
156 |
153 155
|
oveq12d |
|
157 |
|
neg1cn |
|
158 |
157
|
mulid1i |
|
159 |
156 158
|
eqtrdi |
|
160 |
151 159
|
eqtrd |
|
161 |
27 11 13
|
psgnodpmr |
|
162 |
69 139 160 161
|
syl3anc |
|
163 |
129 162
|
chvarvv |
|
164 |
|
eqidd |
|
165 |
|
eqidd |
|
166 |
|
fveq1 |
|
167 |
166
|
oveq1d |
|
168 |
167
|
mpteq2dv |
|
169 |
168
|
oveq2d |
|
170 |
163 164 165 169
|
fmptco |
|
171 |
|
oveq2 |
|
172 |
171
|
fveq1d |
|
173 |
172
|
oveq1d |
|
174 |
173
|
mpteq2dv |
|
175 |
174
|
oveq2d |
|
176 |
175
|
cbvmptv |
|
177 |
176
|
a1i |
|
178 |
135
|
adantr |
|
179 |
136
|
adantr |
|
180 |
27 11 137
|
symgov |
|
181 |
178 179 180
|
syl2anc |
|
182 |
181
|
fveq1d |
|
183 |
75 49
|
sylan2 |
|
184 |
|
fvco3 |
|
185 |
183 184
|
sylan |
|
186 |
182 185
|
eqtrd |
|
187 |
186
|
oveq1d |
|
188 |
116
|
pmtrprfv |
|
189 |
26 7 8 9 188
|
syl13anc |
|
190 |
189
|
ad2antrr |
|
191 |
190
|
oveq1d |
|
192 |
|
oveq2 |
|
193 |
|
oveq2 |
|
194 |
192 193
|
eqeq12d |
|
195 |
10
|
ad2antrr |
|
196 |
|
simpr |
|
197 |
194 195 196
|
rspcdva |
|
198 |
191 197
|
eqtr4d |
|
199 |
|
fveq2 |
|
200 |
199
|
oveq1d |
|
201 |
|
oveq1 |
|
202 |
200 201
|
eqeq12d |
|
203 |
198 202
|
syl5ibrcom |
|
204 |
|
prcom |
|
205 |
204
|
fveq2i |
|
206 |
205
|
fveq1i |
|
207 |
9
|
necomd |
|
208 |
116
|
pmtrprfv |
|
209 |
26 8 7 207 208
|
syl13anc |
|
210 |
206 209
|
syl5eq |
|
211 |
210
|
oveq1d |
|
212 |
211
|
ad2antrr |
|
213 |
212 197
|
eqtrd |
|
214 |
|
fveq2 |
|
215 |
214
|
oveq1d |
|
216 |
|
oveq1 |
|
217 |
215 216
|
eqeq12d |
|
218 |
213 217
|
syl5ibrcom |
|
219 |
218
|
a1dd |
|
220 |
|
neanior |
|
221 |
|
elpri |
|
222 |
221
|
orcomd |
|
223 |
222
|
con3i |
|
224 |
220 223
|
sylbi |
|
225 |
224
|
3adant1 |
|
226 |
116
|
pmtrmvd |
|
227 |
26 113 115 226
|
syl3anc |
|
228 |
227
|
ad2antrr |
|
229 |
228
|
3ad2ant1 |
|
230 |
225 229
|
neleqtrrd |
|
231 |
116
|
pmtrf |
|
232 |
26 113 115 231
|
syl3anc |
|
233 |
232
|
ffnd |
|
234 |
233
|
ad2antrr |
|
235 |
183
|
ffvelrnda |
|
236 |
|
fnelnfp |
|
237 |
234 235 236
|
syl2anc |
|
238 |
237
|
3ad2ant1 |
|
239 |
238
|
necon2bbid |
|
240 |
230 239
|
mpbird |
|
241 |
240
|
oveq1d |
|
242 |
241
|
3exp |
|
243 |
219 242
|
pm2.61dne |
|
244 |
203 243
|
pm2.61dne |
|
245 |
187 244
|
eqtrd |
|
246 |
245
|
mpteq2dva |
|
247 |
246
|
oveq2d |
|
248 |
247
|
mpteq2dva |
|
249 |
170 177 248
|
3eqtrd |
|
250 |
249
|
oveq2d |
|
251 |
124 250
|
eqtrd |
|
252 |
251
|
fveq2d |
|
253 |
105 111 252
|
3eqtrd |
|
254 |
82 253
|
oveq12d |
|
255 |
59
|
a1i |
|
256 |
29 255
|
ssfid |
|
257 |
76
|
ralrimiva |
|
258 |
18 23 256 257
|
gsummptcl |
|
259 |
18 19 4 89
|
grprinv |
|
260 |
99 258 259
|
syl2anc |
|
261 |
254 260
|
eqtrd |
|
262 |
17 65 261
|
3eqtrd |
|