Step |
Hyp |
Ref |
Expression |
1 |
|
wilthlem.t |
|
2 |
|
wilthlem.a |
|
3 |
|
wilthlem2.p |
|
4 |
|
wilthlem2.s |
|
5 |
|
wilthlem2.r |
|
6 |
|
simpr |
|
7 |
|
eleq2 |
|
8 |
|
eleq2 |
|
9 |
8
|
raleqbi1dv |
|
10 |
7 9
|
anbi12d |
|
11 |
10 2
|
elrab2 |
|
12 |
4 11
|
sylib |
|
13 |
12
|
simprd |
|
14 |
13
|
simpld |
|
15 |
14
|
snssd |
|
16 |
15
|
adantr |
|
17 |
6 16
|
eqssd |
|
18 |
17
|
reseq2d |
|
19 |
|
mptresid |
|
20 |
18 19
|
eqtrdi |
|
21 |
20
|
oveq2d |
|
22 |
21
|
oveq1d |
|
23 |
|
prmnn |
|
24 |
3 23
|
syl |
|
25 |
24
|
nncnd |
|
26 |
|
ax-1cn |
|
27 |
|
negsub |
|
28 |
25 26 27
|
sylancl |
|
29 |
|
neg1cn |
|
30 |
|
addcom |
|
31 |
25 29 30
|
sylancl |
|
32 |
28 31
|
eqtr3d |
|
33 |
|
cnring |
|
34 |
1
|
ringmgp |
|
35 |
33 34
|
mp1i |
|
36 |
|
nnm1nn0 |
|
37 |
24 36
|
syl |
|
38 |
37
|
nn0cnd |
|
39 |
|
cnfldbas |
|
40 |
1 39
|
mgpbas |
|
41 |
|
id |
|
42 |
40 41
|
gsumsn |
|
43 |
35 38 38 42
|
syl3anc |
|
44 |
25
|
mulid2d |
|
45 |
44
|
oveq2d |
|
46 |
32 43 45
|
3eqtr4d |
|
47 |
46
|
oveq1d |
|
48 |
|
neg1rr |
|
49 |
48
|
a1i |
|
50 |
24
|
nnrpd |
|
51 |
|
1zzd |
|
52 |
|
modcyc |
|
53 |
49 50 51 52
|
syl3anc |
|
54 |
47 53
|
eqtrd |
|
55 |
54
|
adantr |
|
56 |
22 55
|
eqtrd |
|
57 |
56
|
ex |
|
58 |
|
nss |
|
59 |
|
cnfld1 |
|
60 |
1 59
|
ringidval |
|
61 |
|
cnfldmul |
|
62 |
1 61
|
mgpplusg |
|
63 |
|
cncrng |
|
64 |
1
|
crngmgp |
|
65 |
63 64
|
ax-mp |
|
66 |
65
|
a1i |
|
67 |
4
|
adantr |
|
68 |
|
f1oi |
|
69 |
|
f1of |
|
70 |
68 69
|
ax-mp |
|
71 |
12
|
simpld |
|
72 |
71
|
elpwid |
|
73 |
|
fzssz |
|
74 |
72 73
|
sstrdi |
|
75 |
|
zsscn |
|
76 |
74 75
|
sstrdi |
|
77 |
|
fss |
|
78 |
70 76 77
|
sylancr |
|
79 |
78
|
adantr |
|
80 |
|
fzfi |
|
81 |
|
ssfi |
|
82 |
80 72 81
|
sylancr |
|
83 |
|
1ex |
|
84 |
83
|
a1i |
|
85 |
78 82 84
|
fdmfifsupp |
|
86 |
85
|
adantr |
|
87 |
|
disjdif |
|
88 |
87
|
a1i |
|
89 |
|
undif2 |
|
90 |
|
simprl |
|
91 |
|
oveq1 |
|
92 |
91
|
oveq1d |
|
93 |
92
|
eleq1d |
|
94 |
13
|
simprd |
|
95 |
94
|
adantr |
|
96 |
93 95 90
|
rspcdva |
|
97 |
90 96
|
prssd |
|
98 |
|
ssequn1 |
|
99 |
97 98
|
sylib |
|
100 |
89 99
|
eqtr2id |
|
101 |
40 60 62 66 67 79 86 88 100
|
gsumsplit |
|
102 |
97
|
resabs1d |
|
103 |
102
|
oveq2d |
|
104 |
|
difss |
|
105 |
|
resabs1 |
|
106 |
104 105
|
ax-mp |
|
107 |
106
|
oveq2i |
|
108 |
107
|
a1i |
|
109 |
103 108
|
oveq12d |
|
110 |
101 109
|
eqtrd |
|
111 |
110
|
oveq1d |
|
112 |
|
prfi |
|
113 |
112
|
a1i |
|
114 |
|
zsubrg |
|
115 |
1
|
subrgsubm |
|
116 |
114 115
|
mp1i |
|
117 |
|
f1oi |
|
118 |
|
f1of |
|
119 |
117 118
|
ax-mp |
|
120 |
74
|
adantr |
|
121 |
97 120
|
sstrd |
|
122 |
|
fss |
|
123 |
119 121 122
|
sylancr |
|
124 |
83
|
a1i |
|
125 |
123 113 124
|
fdmfifsupp |
|
126 |
60 66 113 116 123 125
|
gsumsubmcl |
|
127 |
126
|
zred |
|
128 |
|
1red |
|
129 |
72
|
adantr |
|
130 |
129
|
ssdifssd |
|
131 |
|
ssfi |
|
132 |
80 130 131
|
sylancr |
|
133 |
|
f1oi |
|
134 |
|
f1of |
|
135 |
133 134
|
ax-mp |
|
136 |
120
|
ssdifssd |
|
137 |
|
fss |
|
138 |
135 136 137
|
sylancr |
|
139 |
138 132 124
|
fdmfifsupp |
|
140 |
60 66 132 116 138 139
|
gsumsubmcl |
|
141 |
50
|
adantr |
|
142 |
35
|
adantr |
|
143 |
76
|
adantr |
|
144 |
143 90
|
sseldd |
|
145 |
|
id |
|
146 |
40 145
|
gsumsn |
|
147 |
142 144 144 146
|
syl3anc |
|
148 |
147
|
adantr |
|
149 |
|
mptresid |
|
150 |
|
dfsn2 |
|
151 |
|
animorrl |
|
152 |
3
|
adantr |
|
153 |
129 90
|
sseldd |
|
154 |
|
wilthlem1 |
|
155 |
152 153 154
|
syl2anc |
|
156 |
155
|
biimpar |
|
157 |
151 156
|
syldan |
|
158 |
157
|
preq2d |
|
159 |
150 158
|
syl5eq |
|
160 |
159
|
reseq2d |
|
161 |
149 160
|
eqtr3id |
|
162 |
161
|
oveq2d |
|
163 |
|
simpr |
|
164 |
148 162 163
|
3eqtr3d |
|
165 |
164
|
oveq1d |
|
166 |
|
df-pr |
|
167 |
166
|
reseq2i |
|
168 |
|
mptresid |
|
169 |
167 168
|
eqtri |
|
170 |
169
|
oveq2i |
|
171 |
65
|
a1i |
|
172 |
|
snfi |
|
173 |
172
|
a1i |
|
174 |
|
elsni |
|
175 |
174
|
adantl |
|
176 |
144
|
adantr |
|
177 |
175 176
|
eqeltrd |
|
178 |
177
|
adantlr |
|
179 |
143 96
|
sseldd |
|
180 |
179
|
adantr |
|
181 |
|
simprr |
|
182 |
|
velsn |
|
183 |
181 182
|
sylnib |
|
184 |
|
biorf |
|
185 |
183 184
|
syl |
|
186 |
|
ovex |
|
187 |
186
|
elsn |
|
188 |
|
eqcom |
|
189 |
187 188
|
bitri |
|
190 |
|
orcom |
|
191 |
155 189 190
|
3bitr4g |
|
192 |
185 191
|
bitr4d |
|
193 |
192
|
necon3abid |
|
194 |
193
|
biimpa |
|
195 |
|
id |
|
196 |
40 62 171 173 178 180 194 180 195
|
gsumunsn |
|
197 |
170 196
|
syl5eq |
|
198 |
147
|
adantr |
|
199 |
198
|
oveq1d |
|
200 |
197 199
|
eqtrd |
|
201 |
200
|
oveq1d |
|
202 |
153
|
elfzelzd |
|
203 |
24
|
adantr |
|
204 |
|
fzm1ndvds |
|
205 |
203 153 204
|
syl2anc |
|
206 |
|
eqid |
|
207 |
206
|
prmdiv |
|
208 |
152 202 205 207
|
syl3anc |
|
209 |
208
|
simprd |
|
210 |
|
elfznn |
|
211 |
153 210
|
syl |
|
212 |
129 96
|
sseldd |
|
213 |
|
elfznn |
|
214 |
212 213
|
syl |
|
215 |
211 214
|
nnmulcld |
|
216 |
215
|
nnzd |
|
217 |
|
1zzd |
|
218 |
|
moddvds |
|
219 |
203 216 217 218
|
syl3anc |
|
220 |
209 219
|
mpbird |
|
221 |
220
|
adantr |
|
222 |
201 221
|
eqtrd |
|
223 |
165 222
|
pm2.61dane |
|
224 |
|
modmul1 |
|
225 |
127 128 140 141 223 224
|
syl221anc |
|
226 |
140
|
zcnd |
|
227 |
226
|
mulid2d |
|
228 |
227
|
oveq1d |
|
229 |
|
sseqin2 |
|
230 |
97 229
|
sylib |
|
231 |
|
vex |
|
232 |
231
|
prnz |
|
233 |
232
|
a1i |
|
234 |
230 233
|
eqnetrd |
|
235 |
|
disj4 |
|
236 |
235
|
necon2abii |
|
237 |
234 236
|
sylibr |
|
238 |
|
psseq1 |
|
239 |
|
reseq2 |
|
240 |
239
|
oveq2d |
|
241 |
240
|
oveq1d |
|
242 |
241
|
eqeq1d |
|
243 |
238 242
|
imbi12d |
|
244 |
5
|
adantr |
|
245 |
|
ovex |
|
246 |
245
|
elpw2 |
|
247 |
130 246
|
sylibr |
|
248 |
14
|
adantr |
|
249 |
|
eqcom |
|
250 |
182 249
|
bitri |
|
251 |
181 250
|
sylnib |
|
252 |
|
oveq1 |
|
253 |
252
|
oveq1d |
|
254 |
203 36
|
syl |
|
255 |
|
nn0uz |
|
256 |
254 255
|
eleqtrdi |
|
257 |
|
eluzfz2 |
|
258 |
256 257
|
syl |
|
259 |
|
prmz |
|
260 |
152 259
|
syl |
|
261 |
120 248
|
sseldd |
|
262 |
|
1z |
|
263 |
|
zsubcl |
|
264 |
261 262 263
|
sylancl |
|
265 |
|
dvdsmul1 |
|
266 |
260 264 265
|
syl2anc |
|
267 |
203
|
nncnd |
|
268 |
264
|
zcnd |
|
269 |
267 268
|
mulcld |
|
270 |
|
1cnd |
|
271 |
254
|
nn0cnd |
|
272 |
267 270 271
|
subdird |
|
273 |
267 271
|
mulcld |
|
274 |
273 267 270
|
subsubd |
|
275 |
271
|
mulid2d |
|
276 |
275
|
oveq2d |
|
277 |
267 271
|
muls1d |
|
278 |
277
|
oveq1d |
|
279 |
274 276 278
|
3eqtr4d |
|
280 |
272 279
|
eqtrd |
|
281 |
269 270 280
|
mvrraddd |
|
282 |
266 281
|
breqtrrd |
|
283 |
129 248
|
sseldd |
|
284 |
|
fzm1ndvds |
|
285 |
203 283 284
|
syl2anc |
|
286 |
|
eqid |
|
287 |
286
|
prmdiveq |
|
288 |
152 261 285 287
|
syl3anc |
|
289 |
258 282 288
|
mpbi2and |
|
290 |
206
|
prmdivdiv |
|
291 |
152 153 290
|
syl2anc |
|
292 |
289 291
|
eqeq12d |
|
293 |
253 292
|
syl5ibr |
|
294 |
251 293
|
mtod |
|
295 |
|
ioran |
|
296 |
251 294 295
|
sylanbrc |
|
297 |
|
ovex |
|
298 |
297
|
elpr |
|
299 |
296 298
|
sylnibr |
|
300 |
248 299
|
eldifd |
|
301 |
|
eldifi |
|
302 |
95
|
r19.21bi |
|
303 |
301 302
|
sylan2 |
|
304 |
|
eldif |
|
305 |
152
|
adantr |
|
306 |
129
|
sselda |
|
307 |
|
eqid |
|
308 |
307
|
prmdivdiv |
|
309 |
305 306 308
|
syl2anc |
|
310 |
|
oveq1 |
|
311 |
310
|
oveq1d |
|
312 |
311
|
eqeq2d |
|
313 |
309 312
|
syl5ibcom |
|
314 |
|
oveq1 |
|
315 |
314
|
oveq1d |
|
316 |
291
|
adantr |
|
317 |
309 316
|
eqeq12d |
|
318 |
315 317
|
syl5ibr |
|
319 |
313 318
|
orim12d |
|
320 |
|
ovex |
|
321 |
320
|
elpr |
|
322 |
|
vex |
|
323 |
322
|
elpr |
|
324 |
|
orcom |
|
325 |
323 324
|
bitri |
|
326 |
319 321 325
|
3imtr4g |
|
327 |
326
|
con3d |
|
328 |
327
|
impr |
|
329 |
304 328
|
sylan2b |
|
330 |
303 329
|
eldifd |
|
331 |
330
|
ralrimiva |
|
332 |
300 331
|
jca |
|
333 |
|
eleq2 |
|
334 |
|
eleq2 |
|
335 |
334
|
raleqbi1dv |
|
336 |
333 335
|
anbi12d |
|
337 |
336 2
|
elrab2 |
|
338 |
247 332 337
|
sylanbrc |
|
339 |
243 244 338
|
rspcdva |
|
340 |
237 339
|
mpd |
|
341 |
228 340
|
eqtrd |
|
342 |
111 225 341
|
3eqtrd |
|
343 |
342
|
ex |
|
344 |
343
|
exlimdv |
|
345 |
58 344
|
syl5bi |
|
346 |
57 345
|
pm2.61d |
|