Step |
Hyp |
Ref |
Expression |
1 |
|
mplcoe1.p |
|
2 |
|
mplcoe1.d |
|
3 |
|
mplcoe1.z |
|
4 |
|
mplcoe1.o |
|
5 |
|
mplcoe1.i |
|
6 |
|
mplcoe1.b |
|
7 |
|
mplcoe1.n |
|
8 |
|
mplcoe1.r |
|
9 |
|
mplcoe1.x |
|
10 |
|
eqid |
|
11 |
1 10 6 2 9
|
mplelf |
|
12 |
11
|
feqmptd |
|
13 |
|
iftrue |
|
14 |
13
|
adantl |
|
15 |
|
eldif |
|
16 |
|
ssidd |
|
17 |
|
ovex |
|
18 |
2 17
|
rabex2 |
|
19 |
18
|
a1i |
|
20 |
3
|
fvexi |
|
21 |
20
|
a1i |
|
22 |
11 16 19 21
|
suppssr |
|
23 |
22
|
ifeq2d |
|
24 |
|
ifid |
|
25 |
23 24
|
eqtr3di |
|
26 |
15 25
|
sylan2br |
|
27 |
26
|
anassrs |
|
28 |
14 27
|
pm2.61dan |
|
29 |
28
|
mpteq2dva |
|
30 |
12 29
|
eqtr4d |
|
31 |
|
suppssdm |
|
32 |
31 11
|
fssdm |
|
33 |
|
eqid |
|
34 |
|
eqid |
|
35 |
1 33 34 3 6
|
mplelbas |
|
36 |
35
|
simprbi |
|
37 |
9 36
|
syl |
|
38 |
37
|
fsuppimpd |
|
39 |
|
sseq1 |
|
40 |
|
mpteq1 |
|
41 |
|
mpt0 |
|
42 |
40 41
|
eqtrdi |
|
43 |
42
|
oveq2d |
|
44 |
|
eqid |
|
45 |
44
|
gsum0 |
|
46 |
43 45
|
eqtrdi |
|
47 |
|
noel |
|
48 |
|
eleq2 |
|
49 |
47 48
|
mtbiri |
|
50 |
49
|
iffalsed |
|
51 |
50
|
mpteq2dv |
|
52 |
46 51
|
eqeq12d |
|
53 |
39 52
|
imbi12d |
|
54 |
53
|
imbi2d |
|
55 |
|
sseq1 |
|
56 |
|
mpteq1 |
|
57 |
56
|
oveq2d |
|
58 |
|
eleq2 |
|
59 |
58
|
ifbid |
|
60 |
59
|
mpteq2dv |
|
61 |
57 60
|
eqeq12d |
|
62 |
55 61
|
imbi12d |
|
63 |
62
|
imbi2d |
|
64 |
|
sseq1 |
|
65 |
|
mpteq1 |
|
66 |
65
|
oveq2d |
|
67 |
|
eleq2 |
|
68 |
67
|
ifbid |
|
69 |
68
|
mpteq2dv |
|
70 |
66 69
|
eqeq12d |
|
71 |
64 70
|
imbi12d |
|
72 |
71
|
imbi2d |
|
73 |
|
sseq1 |
|
74 |
|
mpteq1 |
|
75 |
74
|
oveq2d |
|
76 |
|
eleq2 |
|
77 |
76
|
ifbid |
|
78 |
77
|
mpteq2dv |
|
79 |
75 78
|
eqeq12d |
|
80 |
73 79
|
imbi12d |
|
81 |
80
|
imbi2d |
|
82 |
|
ringgrp |
|
83 |
8 82
|
syl |
|
84 |
1 2 3 44 5 83
|
mpl0 |
|
85 |
|
fconstmpt |
|
86 |
84 85
|
eqtrdi |
|
87 |
86
|
a1d |
|
88 |
|
ssun1 |
|
89 |
|
sstr2 |
|
90 |
88 89
|
ax-mp |
|
91 |
90
|
imim1i |
|
92 |
|
oveq1 |
|
93 |
|
eqid |
|
94 |
1 5 8
|
mplringd |
|
95 |
|
ringcmn |
|
96 |
94 95
|
syl |
|
97 |
96
|
adantr |
|
98 |
|
simprll |
|
99 |
|
simprr |
|
100 |
99
|
unssad |
|
101 |
100
|
sselda |
|
102 |
5
|
adantr |
|
103 |
8
|
adantr |
|
104 |
1 102 103
|
mpllmodd |
|
105 |
11
|
ffvelcdmda |
|
106 |
1 5 8
|
mplsca |
|
107 |
106
|
adantr |
|
108 |
107
|
fveq2d |
|
109 |
105 108
|
eleqtrd |
|
110 |
|
simpr |
|
111 |
1 6 3 4 2 102 103 110
|
mplmon |
|
112 |
|
eqid |
|
113 |
|
eqid |
|
114 |
6 112 7 113
|
lmodvscl |
|
115 |
104 109 111 114
|
syl3anc |
|
116 |
115
|
adantlr |
|
117 |
101 116
|
syldan |
|
118 |
|
vex |
|
119 |
118
|
a1i |
|
120 |
|
simprlr |
|
121 |
1 5 8
|
mpllmodd |
|
122 |
121
|
adantr |
|
123 |
11
|
adantr |
|
124 |
99
|
unssbd |
|
125 |
118
|
snss |
|
126 |
124 125
|
sylibr |
|
127 |
123 126
|
ffvelcdmd |
|
128 |
106
|
adantr |
|
129 |
128
|
fveq2d |
|
130 |
127 129
|
eleqtrd |
|
131 |
5
|
adantr |
|
132 |
8
|
adantr |
|
133 |
1 6 3 4 2 131 132 126
|
mplmon |
|
134 |
6 112 7 113
|
lmodvscl |
|
135 |
122 130 133 134
|
syl3anc |
|
136 |
|
fveq2 |
|
137 |
|
equequ2 |
|
138 |
137
|
ifbid |
|
139 |
138
|
mpteq2dv |
|
140 |
136 139
|
oveq12d |
|
141 |
6 93 97 98 117 119 120 135 140
|
gsumunsn |
|
142 |
|
eqid |
|
143 |
123
|
ffvelcdmda |
|
144 |
10 3
|
ring0cl |
|
145 |
8 144
|
syl |
|
146 |
145
|
ad2antrr |
|
147 |
143 146
|
ifcld |
|
148 |
147
|
fmpttd |
|
149 |
|
fvex |
|
150 |
149 18
|
elmap |
|
151 |
148 150
|
sylibr |
|
152 |
33 10 2 34 131
|
psrbas |
|
153 |
151 152
|
eleqtrrd |
|
154 |
18
|
mptex |
|
155 |
|
funmpt |
|
156 |
154 155 20
|
3pm3.2i |
|
157 |
156
|
a1i |
|
158 |
|
eldifn |
|
159 |
158
|
adantl |
|
160 |
159
|
iffalsed |
|
161 |
18
|
a1i |
|
162 |
160 161
|
suppss2 |
|
163 |
|
suppssfifsupp |
|
164 |
157 98 162 163
|
syl12anc |
|
165 |
1 33 34 3 6
|
mplelbas |
|
166 |
153 164 165
|
sylanbrc |
|
167 |
1 6 142 93 166 135
|
mpladd |
|
168 |
|
ovexd |
|
169 |
|
eqidd |
|
170 |
|
eqid |
|
171 |
1 7 10 6 170 2 127 133
|
mplvsca |
|
172 |
127
|
adantr |
|
173 |
10 4
|
ringidcl |
|
174 |
173 144
|
ifcld |
|
175 |
8 174
|
syl |
|
176 |
175
|
ad2antrr |
|
177 |
|
fconstmpt |
|
178 |
177
|
a1i |
|
179 |
|
eqidd |
|
180 |
161 172 176 178 179
|
offval2 |
|
181 |
171 180
|
eqtrd |
|
182 |
161 147 168 169 181
|
offval2 |
|
183 |
132 82
|
syl |
|
184 |
10 142 3
|
grplid |
|
185 |
183 127 184
|
syl2anc |
|
186 |
185
|
ad2antrr |
|
187 |
|
simpr |
|
188 |
|
velsn |
|
189 |
187 188
|
sylib |
|
190 |
189
|
fveq2d |
|
191 |
186 190
|
eqtr4d |
|
192 |
120
|
ad2antrr |
|
193 |
189 192
|
eqneltrd |
|
194 |
193
|
iffalsed |
|
195 |
189
|
iftrued |
|
196 |
195
|
oveq2d |
|
197 |
10 170 4
|
ringridm |
|
198 |
132 127 197
|
syl2anc |
|
199 |
198
|
ad2antrr |
|
200 |
196 199
|
eqtrd |
|
201 |
194 200
|
oveq12d |
|
202 |
|
elun2 |
|
203 |
202
|
adantl |
|
204 |
203
|
iftrued |
|
205 |
191 201 204
|
3eqtr4d |
|
206 |
83
|
ad2antrr |
|
207 |
10 142 3
|
grprid |
|
208 |
206 147 207
|
syl2anc |
|
209 |
208
|
adantr |
|
210 |
|
simpr |
|
211 |
210 188
|
sylnib |
|
212 |
211
|
iffalsed |
|
213 |
212
|
oveq2d |
|
214 |
10 170 3
|
ringrz |
|
215 |
132 127 214
|
syl2anc |
|
216 |
215
|
ad2antrr |
|
217 |
213 216
|
eqtrd |
|
218 |
217
|
oveq2d |
|
219 |
|
elun |
|
220 |
|
orcom |
|
221 |
219 220
|
bitri |
|
222 |
|
biorf |
|
223 |
221 222
|
bitr4id |
|
224 |
223
|
adantl |
|
225 |
224
|
ifbid |
|
226 |
209 218 225
|
3eqtr4d |
|
227 |
205 226
|
pm2.61dan |
|
228 |
227
|
mpteq2dva |
|
229 |
167 182 228
|
3eqtrrd |
|
230 |
141 229
|
eqeq12d |
|
231 |
92 230
|
imbitrrid |
|
232 |
231
|
expr |
|
233 |
232
|
a2d |
|
234 |
91 233
|
syl5 |
|
235 |
234
|
expcom |
|
236 |
235
|
a2d |
|
237 |
54 63 72 81 87 236
|
findcard2s |
|
238 |
38 237
|
mpcom |
|
239 |
32 238
|
mpd |
|
240 |
30 239
|
eqtr4d |
|
241 |
32
|
resmptd |
|
242 |
241
|
oveq2d |
|
243 |
115
|
fmpttd |
|
244 |
11 16 19 21
|
suppssr |
|
245 |
244
|
oveq1d |
|
246 |
|
eldifi |
|
247 |
107
|
fveq2d |
|
248 |
3 247
|
eqtrid |
|
249 |
248
|
oveq1d |
|
250 |
|
eqid |
|
251 |
6 112 7 250 44
|
lmod0vs |
|
252 |
104 111 251
|
syl2anc |
|
253 |
249 252
|
eqtrd |
|
254 |
246 253
|
sylan2 |
|
255 |
245 254
|
eqtrd |
|
256 |
255 19
|
suppss2 |
|
257 |
18
|
mptex |
|
258 |
|
funmpt |
|
259 |
|
fvex |
|
260 |
257 258 259
|
3pm3.2i |
|
261 |
260
|
a1i |
|
262 |
|
suppssfifsupp |
|
263 |
261 38 256 262
|
syl12anc |
|
264 |
6 44 96 19 243 256 263
|
gsumres |
|
265 |
242 264
|
eqtr3d |
|
266 |
240 265
|
eqtrd |
|