Step |
Hyp |
Ref |
Expression |
1 |
|
elrspunidl.n |
|
2 |
|
elrspunidl.b |
|
3 |
|
elrspunidl.1 |
|
4 |
|
elrspunidl.x |
|
5 |
|
elrspunidl.r |
|
6 |
|
elrspunidl.i |
|
7 |
6
|
sselda |
|
8 |
|
eqid |
|
9 |
2 8
|
lidlss |
|
10 |
7 9
|
syl |
|
11 |
10
|
ralrimiva |
|
12 |
|
unissb |
|
13 |
11 12
|
sylibr |
|
14 |
1 2 3 4 5 13
|
elrsp |
|
15 |
|
fvexd |
|
16 |
15 6
|
ssexd |
|
17 |
16
|
uniexd |
|
18 |
|
eluni2 |
|
19 |
18
|
biimpi |
|
20 |
19
|
adantl |
|
21 |
20
|
ralrimiva |
|
22 |
|
eleq2 |
|
23 |
22
|
ac6sg |
|
24 |
17 21 23
|
sylc |
|
25 |
24
|
ad3antrrr |
|
26 |
|
simp-5l |
|
27 |
26
|
adantr |
|
28 |
|
ringcmn |
|
29 |
27 5 28
|
3syl |
|
30 |
|
vex |
|
31 |
|
cnvexg |
|
32 |
|
imaexg |
|
33 |
30 31 32
|
mp2b |
|
34 |
33
|
a1i |
|
35 |
5
|
ad7antr |
|
36 |
|
elmapi |
|
37 |
36
|
ad7antlr |
|
38 |
|
cnvimass |
|
39 |
|
fdm |
|
40 |
38 39
|
sseqtrid |
|
41 |
40
|
ad3antlr |
|
42 |
41
|
sselda |
|
43 |
37 42
|
ffvelrnd |
|
44 |
13
|
ad7antr |
|
45 |
44 42
|
sseldd |
|
46 |
2 4
|
ringcl |
|
47 |
35 43 45 46
|
syl3anc |
|
48 |
|
fveq2 |
|
49 |
|
id |
|
50 |
48 49
|
oveq12d |
|
51 |
50
|
cbvmptv |
|
52 |
47 51
|
fmptd |
|
53 |
34
|
mptexd |
|
54 |
52
|
ffund |
|
55 |
|
simp-5r |
|
56 |
|
nfv |
|
57 |
|
nfcv |
|
58 |
|
nfcv |
|
59 |
|
nfmpt1 |
|
60 |
57 58 59
|
nfov |
|
61 |
60
|
nfeq2 |
|
62 |
56 61
|
nfan |
|
63 |
|
nfv |
|
64 |
62 63
|
nfan |
|
65 |
|
nfra1 |
|
66 |
64 65
|
nfan |
|
67 |
|
nfv |
|
68 |
66 67
|
nfan |
|
69 |
|
nfcv |
|
70 |
|
nfcv |
|
71 |
36
|
ad7antlr |
|
72 |
71
|
ffnd |
|
73 |
26 17
|
syl |
|
74 |
73
|
ad2antrr |
|
75 |
3
|
fvexi |
|
76 |
75
|
a1i |
|
77 |
41
|
ssdifd |
|
78 |
77
|
sselda |
|
79 |
72 74 76 78
|
fvdifsupp |
|
80 |
79
|
oveq1d |
|
81 |
5
|
ad7antr |
|
82 |
13
|
ad7antr |
|
83 |
78
|
eldifad |
|
84 |
82 83
|
sseldd |
|
85 |
2 4 3
|
ringlz |
|
86 |
81 84 85
|
syl2anc |
|
87 |
80 86
|
eqtrd |
|
88 |
68 69 70 87 34
|
suppss2f |
|
89 |
|
fsuppsssupp |
|
90 |
53 54 55 88 89
|
syl22anc |
|
91 |
2 3 29 34 52 90
|
gsumcl |
|
92 |
91
|
fmpttd |
|
93 |
2
|
fvexi |
|
94 |
93
|
a1i |
|
95 |
94 16
|
elmapd |
|
96 |
95
|
biimpar |
|
97 |
26 92 96
|
syl2anc |
|
98 |
|
breq1 |
|
99 |
|
oveq2 |
|
100 |
99
|
eqeq2d |
|
101 |
|
fveq1 |
|
102 |
101
|
eleq1d |
|
103 |
102
|
ralbidv |
|
104 |
98 100 103
|
3anbi123d |
|
105 |
104
|
adantl |
|
106 |
26 16
|
syl |
|
107 |
106
|
mptexd |
|
108 |
75
|
a1i |
|
109 |
|
funmpt |
|
110 |
109
|
a1i |
|
111 |
|
simplr |
|
112 |
111
|
ffund |
|
113 |
|
simp-4r |
|
114 |
113
|
fsuppimpd |
|
115 |
|
imafi |
|
116 |
112 114 115
|
syl2anc |
|
117 |
|
nfv |
|
118 |
66 117
|
nfan |
|
119 |
|
simpllr |
|
120 |
119
|
ffund |
|
121 |
|
snssi |
|
122 |
121
|
adantl |
|
123 |
|
sspreima |
|
124 |
120 122 123
|
syl2anc |
|
125 |
|
difpreima |
|
126 |
120 125
|
syl |
|
127 |
124 126
|
sseqtrd |
|
128 |
|
suppssdm |
|
129 |
36
|
ad6antlr |
|
130 |
128 129
|
fssdm |
|
131 |
119
|
fdmd |
|
132 |
130 131
|
sseqtrrd |
|
133 |
|
sseqin2 |
|
134 |
133
|
biimpi |
|
135 |
|
dminss |
|
136 |
134 135
|
eqsstrrdi |
|
137 |
132 136
|
syl |
|
138 |
137
|
sscond |
|
139 |
127 138
|
sstrd |
|
140 |
|
fimacnv |
|
141 |
119 140
|
syl |
|
142 |
141
|
difeq1d |
|
143 |
139 142
|
sseqtrd |
|
144 |
143
|
sselda |
|
145 |
|
ssidd |
|
146 |
73
|
adantr |
|
147 |
75
|
a1i |
|
148 |
129 145 146 147
|
suppssr |
|
149 |
144 148
|
syldan |
|
150 |
149
|
oveq1d |
|
151 |
5
|
ad7antr |
|
152 |
13
|
ad7antr |
|
153 |
40
|
ad3antlr |
|
154 |
153
|
sselda |
|
155 |
152 154
|
sseldd |
|
156 |
151 155 85
|
syl2anc |
|
157 |
150 156
|
eqtrd |
|
158 |
118 157
|
mpteq2da |
|
159 |
158
|
oveq2d |
|
160 |
5 28
|
syl |
|
161 |
160
|
cmnmndd |
|
162 |
161
|
ad6antr |
|
163 |
3
|
gsumz |
|
164 |
162 33 163
|
sylancl |
|
165 |
159 164
|
eqtrd |
|
166 |
165 106
|
suppss2 |
|
167 |
116 166
|
ssfid |
|
168 |
|
isfsupp |
|
169 |
168
|
biimpar |
|
170 |
107 108 110 167 169
|
syl22anc |
|
171 |
|
simpllr |
|
172 |
26 160
|
syl |
|
173 |
5
|
ad6antr |
|
174 |
36
|
ad5antlr |
|
175 |
174
|
ffvelrnda |
|
176 |
26 13
|
syl |
|
177 |
176
|
sselda |
|
178 |
2 4
|
ringcl |
|
179 |
173 175 177 178
|
syl3anc |
|
180 |
|
eqid |
|
181 |
66 179 180
|
fmptdf |
|
182 |
73
|
mptexd |
|
183 |
|
funmpt |
|
184 |
183
|
a1i |
|
185 |
|
nfcv |
|
186 |
174
|
adantr |
|
187 |
186
|
ffnd |
|
188 |
73
|
adantr |
|
189 |
75
|
a1i |
|
190 |
|
simpr |
|
191 |
187 188 189 190
|
fvdifsupp |
|
192 |
191
|
oveq1d |
|
193 |
5
|
ad6antr |
|
194 |
176
|
adantr |
|
195 |
190
|
eldifad |
|
196 |
194 195
|
sseldd |
|
197 |
193 196 85
|
syl2anc |
|
198 |
192 197
|
eqtrd |
|
199 |
66 185 70 198 73
|
suppss2f |
|
200 |
|
fsuppsssupp |
|
201 |
182 184 113 199 200
|
syl22anc |
|
202 |
|
sndisj |
|
203 |
|
disjpreima |
|
204 |
112 202 203
|
sylancl |
|
205 |
|
iunid |
|
206 |
205
|
imaeq2i |
|
207 |
|
iunpreima |
|
208 |
112 207
|
syl |
|
209 |
140
|
ad2antlr |
|
210 |
206 208 209
|
3eqtr3a |
|
211 |
2 3 172 73 106 181 201 204 210
|
gsumpart |
|
212 |
41
|
resmptd |
|
213 |
212
|
oveq2d |
|
214 |
213
|
mpteq2dva |
|
215 |
214
|
oveq2d |
|
216 |
171 211 215
|
3eqtrd |
|
217 |
|
eqid |
|
218 |
|
simpr |
|
219 |
218
|
sneqd |
|
220 |
219
|
imaeq2d |
|
221 |
220
|
mpteq1d |
|
222 |
221
|
oveq2d |
|
223 |
|
simpr |
|
224 |
|
ovexd |
|
225 |
217 222 223 224
|
fvmptd2 |
|
226 |
160
|
ad6antr |
|
227 |
30
|
cnvex |
|
228 |
227
|
imaex |
|
229 |
228
|
a1i |
|
230 |
5
|
ad6antr |
|
231 |
26 6
|
syl |
|
232 |
231
|
sselda |
|
233 |
8
|
lidlsubg |
|
234 |
|
subgsubm |
|
235 |
233 234
|
syl |
|
236 |
230 232 235
|
syl2anc |
|
237 |
230
|
adantr |
|
238 |
232
|
adantr |
|
239 |
36
|
ad7antlr |
|
240 |
|
cnvimass |
|
241 |
240 39
|
sseqtrid |
|
242 |
241
|
ad3antlr |
|
243 |
242
|
sselda |
|
244 |
239 243
|
ffvelrnd |
|
245 |
|
fveq2 |
|
246 |
49 245
|
eleq12d |
|
247 |
|
simpllr |
|
248 |
246 247 243
|
rspcdva |
|
249 |
|
simp-4r |
|
250 |
249
|
ffnd |
|
251 |
|
elpreima |
|
252 |
251
|
biimpa |
|
253 |
|
elsni |
|
254 |
252 253
|
simpl2im |
|
255 |
250 254
|
sylancom |
|
256 |
248 255
|
eleqtrd |
|
257 |
8 2 4
|
lidlmcl |
|
258 |
237 238 244 256 257
|
syl22anc |
|
259 |
50
|
cbvmptv |
|
260 |
258 259
|
fmptd |
|
261 |
229
|
mptexd |
|
262 |
260
|
ffund |
|
263 |
|
simp-5r |
|
264 |
|
nfv |
|
265 |
66 264
|
nfan |
|
266 |
|
nfcv |
|
267 |
36
|
ad7antlr |
|
268 |
267
|
ffnd |
|
269 |
73
|
ad2antrr |
|
270 |
75
|
a1i |
|
271 |
242
|
ssdifd |
|
272 |
271
|
sselda |
|
273 |
268 269 270 272
|
fvdifsupp |
|
274 |
273
|
oveq1d |
|
275 |
13
|
ad7antr |
|
276 |
272
|
eldifad |
|
277 |
275 276
|
sseldd |
|
278 |
230 277 85
|
syl2an2r |
|
279 |
274 278
|
eqtrd |
|
280 |
265 266 70 279 229
|
suppss2f |
|
281 |
|
fsuppsssupp |
|
282 |
261 262 263 280 281
|
syl22anc |
|
283 |
3 226 229 236 260 282
|
gsumsubmcl |
|
284 |
225 283
|
eqeltrd |
|
285 |
284
|
ralrimiva |
|
286 |
170 216 285
|
3jca |
|
287 |
97 105 286
|
rspcedvd |
|
288 |
287
|
anasss |
|
289 |
25 288
|
exlimddv |
|
290 |
289
|
anasss |
|
291 |
290
|
r19.29an |
|
292 |
5
|
ad4antr |
|
293 |
292
|
adantr |
|
294 |
|
eqid |
|
295 |
294
|
zrhrhm |
|
296 |
|
zringbas |
|
297 |
296 2
|
rhmf |
|
298 |
293 295 297
|
3syl |
|
299 |
|
simp-5r |
|
300 |
75
|
a1i |
|
301 |
|
ssv |
|
302 |
|
ssdif |
|
303 |
301 302
|
ax-mp |
|
304 |
303
|
sseli |
|
305 |
304
|
adantl |
|
306 |
|
simp-4r |
|
307 |
299 300 305 306
|
fsuppinisegfi |
|
308 |
|
hashcl |
|
309 |
307 308
|
syl |
|
310 |
309
|
nn0zd |
|
311 |
298 310
|
ffvelrnd |
|
312 |
|
eqid |
|
313 |
311 312
|
fmptd |
|
314 |
2 3
|
ring0cl |
|
315 |
|
fconst6g |
|
316 |
292 314 315
|
3syl |
|
317 |
|
disjdif |
|
318 |
317
|
a1i |
|
319 |
313 316 318
|
fun2d |
|
320 |
|
simplll |
|
321 |
94 16
|
elmapd |
|
322 |
321
|
biimpa |
|
323 |
320 322
|
syl |
|
324 |
323
|
ffnd |
|
325 |
|
elssuni |
|
326 |
325
|
adantl |
|
327 |
326
|
sseld |
|
328 |
327
|
ralimdva |
|
329 |
328
|
imp |
|
330 |
|
fnfvrnss |
|
331 |
324 329 330
|
syl2anc |
|
332 |
331
|
ssdifssd |
|
333 |
|
undif |
|
334 |
332 333
|
sylib |
|
335 |
334
|
feq2d |
|
336 |
319 335
|
mpbid |
|
337 |
93
|
a1i |
|
338 |
17
|
ad4antr |
|
339 |
337 338
|
elmapd |
|
340 |
336 339
|
mpbird |
|
341 |
|
breq1 |
|
342 |
|
fveq1 |
|
343 |
342
|
oveq1d |
|
344 |
343
|
mpteq2dv |
|
345 |
344
|
oveq2d |
|
346 |
345
|
eqeq2d |
|
347 |
341 346
|
anbi12d |
|
348 |
347
|
adantl |
|
349 |
319
|
ffund |
|
350 |
340
|
elexd |
|
351 |
75
|
a1i |
|
352 |
323
|
ffund |
|
353 |
320
|
simprd |
|
354 |
|
simpllr |
|
355 |
|
fsupprnfi |
|
356 |
|
diffi |
|
357 |
355 356
|
syl |
|
358 |
352 353 351 354 357
|
syl22anc |
|
359 |
313 358 351
|
fdmfifsupp |
|
360 |
13
|
ssdifssd |
|
361 |
360
|
ad4antr |
|
362 |
337 361
|
ssexd |
|
363 |
362 351
|
fczfsuppd |
|
364 |
359 363
|
fsuppun |
|
365 |
|
funisfsupp |
|
366 |
365
|
biimpar |
|
367 |
349 350 351 364 366
|
syl31anc |
|
368 |
|
fvex |
|
369 |
368 312
|
fnmpti |
|
370 |
369
|
a1i |
|
371 |
|
fnconstg |
|
372 |
75 371
|
ax-mp |
|
373 |
372
|
a1i |
|
374 |
317
|
a1i |
|
375 |
|
simpr |
|
376 |
370 373 374 375
|
fvun1d |
|
377 |
|
sneq |
|
378 |
377
|
imaeq2d |
|
379 |
378
|
fveq2d |
|
380 |
379
|
fveq2d |
|
381 |
|
fvexd |
|
382 |
312 380 375 381
|
fvmptd3 |
|
383 |
376 382
|
eqtrd |
|
384 |
383
|
oveq1d |
|
385 |
384
|
mpteq2dva |
|
386 |
385
|
oveq2d |
|
387 |
292 28
|
syl |
|
388 |
317
|
a1i |
|
389 |
|
fvun2 |
|
390 |
369 372 389
|
mp3an12 |
|
391 |
388 390
|
sylancom |
|
392 |
75
|
fvconst2 |
|
393 |
392
|
adantl |
|
394 |
391 393
|
eqtrd |
|
395 |
394
|
oveq1d |
|
396 |
361
|
sselda |
|
397 |
292 396 85
|
syl2an2r |
|
398 |
395 397
|
eqtrd |
|
399 |
292
|
adantr |
|
400 |
336
|
ffvelrnda |
|
401 |
13
|
ad4antr |
|
402 |
401
|
sselda |
|
403 |
2 4
|
ringcl |
|
404 |
399 400 402 403
|
syl3anc |
|
405 |
2 3 387 338 398 358 404 332
|
gsummptres2 |
|
406 |
|
eqid |
|
407 |
2 3 406 387 323 354
|
gsumhashmul |
|
408 |
|
simplr |
|
409 |
292
|
adantr |
|
410 |
353
|
adantr |
|
411 |
75
|
a1i |
|
412 |
303 375
|
sselid |
|
413 |
354
|
adantr |
|
414 |
410 411 412 413
|
fsuppinisegfi |
|
415 |
|
hashcl |
|
416 |
414 415
|
syl |
|
417 |
416
|
nn0zd |
|
418 |
332 401
|
sstrd |
|
419 |
418
|
sselda |
|
420 |
|
eqid |
|
421 |
294 406 420
|
zrhmulg |
|
422 |
421
|
adantr |
|
423 |
422
|
oveq1d |
|
424 |
|
simpll |
|
425 |
|
simplr |
|
426 |
2 420
|
ringidcl |
|
427 |
426
|
ad2antrr |
|
428 |
|
simpr |
|
429 |
2 406 4
|
mulgass2 |
|
430 |
424 425 427 428 429
|
syl13anc |
|
431 |
2 4 420
|
ringlidm |
|
432 |
424 431
|
sylancom |
|
433 |
432
|
oveq2d |
|
434 |
423 430 433
|
3eqtrd |
|
435 |
409 417 419 434
|
syl21anc |
|
436 |
435
|
mpteq2dva |
|
437 |
436
|
oveq2d |
|
438 |
407 408 437
|
3eqtr4d |
|
439 |
386 405 438
|
3eqtr4rd |
|
440 |
367 439
|
jca |
|
441 |
340 348 440
|
rspcedvd |
|
442 |
441
|
exp41 |
|
443 |
442
|
3imp2 |
|
444 |
443
|
r19.29an |
|
445 |
291 444
|
impbida |
|
446 |
14 445
|
bitrd |
|