Step |
Hyp |
Ref |
Expression |
1 |
|
stoweidlem59.1 |
|
2 |
|
stoweidlem59.2 |
|
3 |
|
stoweidlem59.3 |
|
4 |
|
stoweidlem59.4 |
|
5 |
|
stoweidlem59.5 |
|
6 |
|
stoweidlem59.6 |
|
7 |
|
stoweidlem59.7 |
|
8 |
|
stoweidlem59.8 |
|
9 |
|
stoweidlem59.9 |
|
10 |
|
stoweidlem59.10 |
|
11 |
|
stoweidlem59.11 |
|
12 |
|
stoweidlem59.12 |
|
13 |
|
stoweidlem59.13 |
|
14 |
|
stoweidlem59.14 |
|
15 |
|
stoweidlem59.15 |
|
16 |
|
stoweidlem59.16 |
|
17 |
|
stoweidlem59.17 |
|
18 |
|
stoweidlem59.18 |
|
19 |
|
stoweidlem59.19 |
|
20 |
|
nfrab1 |
|
21 |
8 20
|
nfcxfr |
|
22 |
|
nfcv |
|
23 |
|
nfv |
|
24 |
|
nfv |
|
25 |
|
fveq1 |
|
26 |
25
|
breq1d |
|
27 |
26
|
ralbidv |
|
28 |
25
|
breq2d |
|
29 |
28
|
ralbidv |
|
30 |
27 29
|
anbi12d |
|
31 |
21 22 23 24 30
|
cbvrabw |
|
32 |
|
ovexd |
|
33 |
11 5
|
sseqtrdi |
|
34 |
32 33
|
ssexd |
|
35 |
8 34
|
rabexd |
|
36 |
31 35
|
rabexd |
|
37 |
36
|
ralrimivw |
|
38 |
9
|
fnmpt |
|
39 |
37 38
|
syl |
|
40 |
|
fzfi |
|
41 |
|
fnfi |
|
42 |
39 40 41
|
sylancl |
|
43 |
|
rnfi |
|
44 |
42 43
|
syl |
|
45 |
|
fnchoice |
|
46 |
44 45
|
syl |
|
47 |
|
simprl |
|
48 |
|
ovex |
|
49 |
48
|
mptex |
|
50 |
9 49
|
eqeltri |
|
51 |
50
|
rnex |
|
52 |
|
fnex |
|
53 |
47 51 52
|
sylancl |
|
54 |
|
coexg |
|
55 |
53 50 54
|
sylancl |
|
56 |
|
dffn3 |
|
57 |
47 56
|
sylib |
|
58 |
|
nfv |
|
59 |
|
nfv |
|
60 |
|
nfra1 |
|
61 |
59 60
|
nfan |
|
62 |
58 61
|
nfan |
|
63 |
|
simplrr |
|
64 |
|
simpr |
|
65 |
|
fvelrnb |
|
66 |
|
nfv |
|
67 |
|
nfmpt1 |
|
68 |
9 67
|
nfcxfr |
|
69 |
|
nfcv |
|
70 |
68 69
|
nffv |
|
71 |
|
nfcv |
|
72 |
70 71
|
nfeq |
|
73 |
|
fveq2 |
|
74 |
73
|
eqeq1d |
|
75 |
66 72 74
|
cbvrexw |
|
76 |
65 75
|
bitr4di |
|
77 |
39 76
|
syl |
|
78 |
77
|
biimpa |
|
79 |
|
simp3 |
|
80 |
|
simpr |
|
81 |
36
|
adantr |
|
82 |
9
|
fvmpt2 |
|
83 |
80 81 82
|
syl2anc |
|
84 |
|
nfcv |
|
85 |
|
nfrab1 |
|
86 |
84 85
|
nfmpt |
|
87 |
6 86
|
nfcxfr |
|
88 |
|
nfcv |
|
89 |
87 88
|
nffv |
|
90 |
|
nfcv |
|
91 |
|
nfrab1 |
|
92 |
84 91
|
nfmpt |
|
93 |
7 92
|
nfcxfr |
|
94 |
93 88
|
nffv |
|
95 |
90 94
|
nfdif |
|
96 |
|
nfv |
|
97 |
2 96
|
nfan |
|
98 |
10
|
adantr |
|
99 |
11
|
adantr |
|
100 |
12
|
3adant1r |
|
101 |
13
|
3adant1r |
|
102 |
14
|
adantlr |
|
103 |
15
|
adantlr |
|
104 |
10
|
uniexd |
|
105 |
4 104
|
eqeltrid |
|
106 |
105
|
adantr |
|
107 |
|
rabexg |
|
108 |
106 107
|
syl |
|
109 |
7
|
fvmpt2 |
|
110 |
80 108 109
|
syl2anc |
|
111 |
|
eqid |
|
112 |
|
elfzelz |
|
113 |
112
|
zred |
|
114 |
|
3re |
|
115 |
|
3ne0 |
|
116 |
114 115
|
rereccli |
|
117 |
|
readdcl |
|
118 |
113 116 117
|
sylancl |
|
119 |
118
|
adantl |
|
120 |
17
|
rpred |
|
121 |
120
|
adantr |
|
122 |
119 121
|
remulcld |
|
123 |
16 5
|
eleqtrdi |
|
124 |
123
|
adantr |
|
125 |
1 3 4 111 122 124
|
rfcnpre3 |
|
126 |
110 125
|
eqeltrd |
|
127 |
|
rabexg |
|
128 |
106 127
|
syl |
|
129 |
6
|
fvmpt2 |
|
130 |
80 128 129
|
syl2anc |
|
131 |
|
eqid |
|
132 |
|
resubcl |
|
133 |
113 116 132
|
sylancl |
|
134 |
133
|
adantl |
|
135 |
134 121
|
remulcld |
|
136 |
1 3 4 131 135 124
|
rfcnpre4 |
|
137 |
130 136
|
eqeltrd |
|
138 |
135
|
adantr |
|
139 |
122
|
adantr |
|
140 |
3 4 5 16
|
fcnre |
|
141 |
140
|
ad2antrr |
|
142 |
|
ssrab2 |
|
143 |
110 142
|
eqsstrdi |
|
144 |
143
|
sselda |
|
145 |
141 144
|
ffvelrnd |
|
146 |
116 132
|
mpan2 |
|
147 |
|
id |
|
148 |
116 117
|
mpan2 |
|
149 |
|
3pos |
|
150 |
114 149
|
recgt0ii |
|
151 |
116 150
|
elrpii |
|
152 |
|
ltsubrp |
|
153 |
151 152
|
mpan2 |
|
154 |
|
ltaddrp |
|
155 |
151 154
|
mpan2 |
|
156 |
146 147 148 153 155
|
lttrd |
|
157 |
113 156
|
syl |
|
158 |
157
|
adantl |
|
159 |
17
|
rpregt0d |
|
160 |
159
|
adantr |
|
161 |
|
ltmul1 |
|
162 |
134 119 160 161
|
syl3anc |
|
163 |
158 162
|
mpbid |
|
164 |
163
|
adantr |
|
165 |
110
|
eleq2d |
|
166 |
165
|
biimpa |
|
167 |
|
rabid |
|
168 |
166 167
|
sylib |
|
169 |
168
|
simprd |
|
170 |
138 139 145 164 169
|
ltletrd |
|
171 |
138 145
|
ltnled |
|
172 |
170 171
|
mpbid |
|
173 |
172
|
intnand |
|
174 |
|
rabid |
|
175 |
173 174
|
sylnibr |
|
176 |
130
|
adantr |
|
177 |
175 176
|
neleqtrrd |
|
178 |
177
|
ex |
|
179 |
97 178
|
ralrimi |
|
180 |
|
disj |
|
181 |
|
nfcv |
|
182 |
89
|
nfcri |
|
183 |
182
|
nfn |
|
184 |
|
nfv |
|
185 |
|
eleq1 |
|
186 |
185
|
notbid |
|
187 |
181 94 183 184 186
|
cbvralfw |
|
188 |
180 187
|
bitri |
|
189 |
179 188
|
sylibr |
|
190 |
|
eqid |
|
191 |
19
|
nnrpd |
|
192 |
17 191
|
rpdivcld |
|
193 |
192
|
adantr |
|
194 |
120 19
|
nndivred |
|
195 |
116
|
a1i |
|
196 |
19
|
nnge1d |
|
197 |
|
1re |
|
198 |
|
0lt1 |
|
199 |
197 198
|
pm3.2i |
|
200 |
199
|
a1i |
|
201 |
19
|
nnred |
|
202 |
19
|
nngt0d |
|
203 |
|
lediv2 |
|
204 |
200 201 202 159 203
|
syl121anc |
|
205 |
196 204
|
mpbid |
|
206 |
17
|
rpcnd |
|
207 |
206
|
div1d |
|
208 |
205 207
|
breqtrd |
|
209 |
194 120 195 208 18
|
lelttrd |
|
210 |
209
|
adantr |
|
211 |
89 95 97 3 4 5 98 99 100 101 102 103 126 137 189 190 193 210
|
stoweidlem58 |
|
212 |
|
df-rex |
|
213 |
211 212
|
sylib |
|
214 |
|
simprl |
|
215 |
|
simprr1 |
|
216 |
|
fveq1 |
|
217 |
216
|
breq2d |
|
218 |
216
|
breq1d |
|
219 |
217 218
|
anbi12d |
|
220 |
219
|
ralbidv |
|
221 |
220 8
|
elrab2 |
|
222 |
214 215 221
|
sylanbrc |
|
223 |
|
simprr2 |
|
224 |
|
simprr3 |
|
225 |
223 224
|
jca |
|
226 |
|
nfcv |
|
227 |
|
nfv |
|
228 |
216
|
breq1d |
|
229 |
228
|
ralbidv |
|
230 |
216
|
breq2d |
|
231 |
230
|
ralbidv |
|
232 |
229 231
|
anbi12d |
|
233 |
226 21 227 232
|
elrabf |
|
234 |
222 225 233
|
sylanbrc |
|
235 |
234
|
ex |
|
236 |
235
|
eximdv |
|
237 |
213 236
|
mpd |
|
238 |
|
ne0i |
|
239 |
238
|
exlimiv |
|
240 |
237 239
|
syl |
|
241 |
83 240
|
eqnetrd |
|
242 |
241
|
3adant3 |
|
243 |
79 242
|
eqnetrrd |
|
244 |
243
|
3exp |
|
245 |
244
|
rexlimdv |
|
246 |
245
|
adantr |
|
247 |
78 246
|
mpd |
|
248 |
247
|
adantlr |
|
249 |
|
rsp |
|
250 |
63 64 248 249
|
syl3c |
|
251 |
250
|
ex |
|
252 |
62 251
|
ralrimi |
|
253 |
|
chfnrn |
|
254 |
47 252 253
|
syl2anc |
|
255 |
|
nfv |
|
256 |
|
nfcv |
|
257 |
|
nfcv |
|
258 |
|
nfrab1 |
|
259 |
257 258
|
nfmpt |
|
260 |
9 259
|
nfcxfr |
|
261 |
260
|
nfrn |
|
262 |
256 261
|
nffn |
|
263 |
|
nfv |
|
264 |
261 263
|
nfralw |
|
265 |
262 264
|
nfan |
|
266 |
255 265
|
nfan |
|
267 |
261
|
nfuni |
|
268 |
|
fnunirn |
|
269 |
|
nfcv |
|
270 |
68 269
|
nffv |
|
271 |
270
|
nfcri |
|
272 |
|
nfv |
|
273 |
|
fveq2 |
|
274 |
273
|
eleq2d |
|
275 |
271 272 274
|
cbvrexw |
|
276 |
268 275
|
syl6bb |
|
277 |
39 276
|
syl |
|
278 |
277
|
biimpa |
|
279 |
|
nfv |
|
280 |
68
|
nfrn |
|
281 |
280
|
nfuni |
|
282 |
281
|
nfcri |
|
283 |
279 282
|
nfan |
|
284 |
|
nfv |
|
285 |
|
simp1l |
|
286 |
|
simp2 |
|
287 |
|
simp3 |
|
288 |
83
|
eleq2d |
|
289 |
288
|
biimpa |
|
290 |
|
rabid |
|
291 |
289 290
|
sylib |
|
292 |
291
|
simpld |
|
293 |
285 286 287 292
|
syl21anc |
|
294 |
293
|
3exp |
|
295 |
283 284 294
|
rexlimd |
|
296 |
278 295
|
mpd |
|
297 |
296
|
adantlr |
|
298 |
297
|
ex |
|
299 |
266 267 21 298
|
ssrd |
|
300 |
|
ssrab2 |
|
301 |
8 300
|
eqsstri |
|
302 |
299 301
|
sstrdi |
|
303 |
254 302
|
sstrd |
|
304 |
57 303
|
fssd |
|
305 |
|
dffn3 |
|
306 |
39 305
|
sylib |
|
307 |
306
|
adantr |
|
308 |
|
fco |
|
309 |
304 307 308
|
syl2anc |
|
310 |
|
nfcv |
|
311 |
310 280
|
nffn |
|
312 |
|
nfv |
|
313 |
280 312
|
nfralw |
|
314 |
311 313
|
nfan |
|
315 |
279 314
|
nfan |
|
316 |
|
simpll |
|
317 |
|
simpr |
|
318 |
39
|
ad2antrr |
|
319 |
|
fvco2 |
|
320 |
318 319
|
sylancom |
|
321 |
|
simplrr |
|
322 |
|
fnfun |
|
323 |
39 322
|
syl |
|
324 |
323
|
ad2antrr |
|
325 |
39
|
fndmd |
|
326 |
325
|
adantr |
|
327 |
80 326
|
eleqtrrd |
|
328 |
327
|
adantlr |
|
329 |
|
fvelrn |
|
330 |
324 328 329
|
syl2anc |
|
331 |
321 330
|
jca |
|
332 |
241
|
adantlr |
|
333 |
|
neeq1 |
|
334 |
|
fveq2 |
|
335 |
|
id |
|
336 |
334 335
|
eleq12d |
|
337 |
333 336
|
imbi12d |
|
338 |
337
|
rspccva |
|
339 |
331 332 338
|
sylc |
|
340 |
320 339
|
eqeltrd |
|
341 |
256 260
|
nfco |
|
342 |
|
nfcv |
|
343 |
341 342
|
nffv |
|
344 |
|
nfv |
|
345 |
260 342
|
nffv |
|
346 |
343 345
|
nfel |
|
347 |
344 346
|
nfan |
|
348 |
343 21
|
nfel |
|
349 |
347 348
|
nfim |
|
350 |
|
eleq1 |
|
351 |
350
|
anbi2d |
|
352 |
|
eleq1 |
|
353 |
351 352
|
imbi12d |
|
354 |
343 349 353 292
|
vtoclgf |
|
355 |
354
|
anabsi7 |
|
356 |
316 317 340 355
|
syl21anc |
|
357 |
8
|
eleq2i |
|
358 |
|
nfcv |
|
359 |
|
nfcv |
|
360 |
|
nfcv |
|
361 |
|
nfcv |
|
362 |
|
nfcv |
|
363 |
343 362
|
nffv |
|
364 |
360 361 363
|
nfbr |
|
365 |
|
nfcv |
|
366 |
363 361 365
|
nfbr |
|
367 |
364 366
|
nfan |
|
368 |
359 367
|
nfralw |
|
369 |
|
nfcv |
|
370 |
|
nfcv |
|
371 |
|
nfra1 |
|
372 |
|
nfra1 |
|
373 |
371 372
|
nfan |
|
374 |
|
nfra1 |
|
375 |
|
nfcv |
|
376 |
374 375
|
nfrabw |
|
377 |
8 376
|
nfcxfr |
|
378 |
373 377
|
nfrabw |
|
379 |
84 378
|
nfmpt |
|
380 |
9 379
|
nfcxfr |
|
381 |
370 380
|
nfco |
|
382 |
381 88
|
nffv |
|
383 |
369 382
|
nfeq |
|
384 |
|
fveq1 |
|
385 |
384
|
breq2d |
|
386 |
384
|
breq1d |
|
387 |
385 386
|
anbi12d |
|
388 |
383 387
|
ralbid |
|
389 |
343 358 368 388
|
elrabf |
|
390 |
357 389
|
bitri |
|
391 |
356 390
|
sylib |
|
392 |
391
|
simprd |
|
393 |
|
nfcv |
|
394 |
|
nfcv |
|
395 |
|
nfcv |
|
396 |
363 394 395
|
nfbr |
|
397 |
393 396
|
nfralw |
|
398 |
347 397
|
nfim |
|
399 |
384
|
breq1d |
|
400 |
383 399
|
ralbid |
|
401 |
351 400
|
imbi12d |
|
402 |
291
|
simprd |
|
403 |
402
|
simpld |
|
404 |
343 398 401 403
|
vtoclgf |
|
405 |
404
|
anabsi7 |
|
406 |
316 317 340 405
|
syl21anc |
|
407 |
|
nfcv |
|
408 |
|
nfcv |
|
409 |
408 394 363
|
nfbr |
|
410 |
407 409
|
nfralw |
|
411 |
347 410
|
nfim |
|
412 |
384
|
breq2d |
|
413 |
383 412
|
ralbid |
|
414 |
351 413
|
imbi12d |
|
415 |
402
|
simprd |
|
416 |
343 411 414 415
|
vtoclgf |
|
417 |
416
|
anabsi7 |
|
418 |
316 317 340 417
|
syl21anc |
|
419 |
392 406 418
|
3jca |
|
420 |
419
|
ex |
|
421 |
315 420
|
ralrimi |
|
422 |
309 421
|
jca |
|
423 |
|
feq1 |
|
424 |
|
nfcv |
|
425 |
310 68
|
nfco |
|
426 |
424 425
|
nfeq |
|
427 |
|
nfcv |
|
428 |
427 381
|
nfeq |
|
429 |
|
fveq1 |
|
430 |
429
|
fveq1d |
|
431 |
430
|
breq2d |
|
432 |
430
|
breq1d |
|
433 |
431 432
|
anbi12d |
|
434 |
428 433
|
ralbid |
|
435 |
430
|
breq1d |
|
436 |
428 435
|
ralbid |
|
437 |
430
|
breq2d |
|
438 |
428 437
|
ralbid |
|
439 |
434 436 438
|
3anbi123d |
|
440 |
426 439
|
ralbid |
|
441 |
423 440
|
anbi12d |
|
442 |
441
|
spcegv |
|
443 |
55 422 442
|
sylc |
|
444 |
46 443
|
exlimddv |
|