Step |
Hyp |
Ref |
Expression |
1 |
|
dvnprodlem1.c |
|
2 |
|
dvnprodlem1.j |
|
3 |
|
dvnprodlem1.d |
|
4 |
|
dvnprodlem1.t |
|
5 |
|
dvnprodlem1.z |
|
6 |
|
dvnprodlem1.zr |
|
7 |
|
dvnprodlem1.rzt |
|
8 |
|
eqidd |
|
9 |
|
0zd |
|
10 |
2
|
nn0zd |
|
11 |
10
|
adantr |
|
12 |
|
fzssz |
|
13 |
12
|
a1i |
|
14 |
|
oveq2 |
|
15 |
|
rabeq |
|
16 |
14 15
|
syl |
|
17 |
|
sumeq1 |
|
18 |
17
|
eqeq1d |
|
19 |
18
|
rabbidv |
|
20 |
16 19
|
eqtrd |
|
21 |
20
|
mpteq2dv |
|
22 |
|
ssexg |
|
23 |
7 4 22
|
syl2anc |
|
24 |
|
elpwg |
|
25 |
23 24
|
syl |
|
26 |
7 25
|
mpbird |
|
27 |
|
nn0ex |
|
28 |
27
|
mptex |
|
29 |
28
|
a1i |
|
30 |
1 21 26 29
|
fvmptd3 |
|
31 |
|
oveq2 |
|
32 |
31
|
oveq1d |
|
33 |
|
rabeq |
|
34 |
32 33
|
syl |
|
35 |
|
eqeq2 |
|
36 |
35
|
rabbidv |
|
37 |
34 36
|
eqtrd |
|
38 |
37
|
adantl |
|
39 |
|
ovex |
|
40 |
39
|
rabex |
|
41 |
40
|
a1i |
|
42 |
30 38 2 41
|
fvmptd |
|
43 |
|
ssrab2 |
|
44 |
43
|
a1i |
|
45 |
42 44
|
eqsstrd |
|
46 |
45
|
adantr |
|
47 |
|
simpr |
|
48 |
46 47
|
sseldd |
|
49 |
|
elmapi |
|
50 |
48 49
|
syl |
|
51 |
|
snidg |
|
52 |
5 51
|
syl |
|
53 |
|
elun2 |
|
54 |
52 53
|
syl |
|
55 |
54
|
adantr |
|
56 |
50 55
|
ffvelrnd |
|
57 |
13 56
|
sseldd |
|
58 |
11 57
|
zsubcld |
|
59 |
9 11 58
|
3jca |
|
60 |
|
elfzle2 |
|
61 |
56 60
|
syl |
|
62 |
11
|
zred |
|
63 |
57
|
zred |
|
64 |
62 63
|
subge0d |
|
65 |
61 64
|
mpbird |
|
66 |
|
elfzle1 |
|
67 |
56 66
|
syl |
|
68 |
62 63
|
subge02d |
|
69 |
67 68
|
mpbid |
|
70 |
59 65 69
|
jca32 |
|
71 |
|
elfz2 |
|
72 |
70 71
|
sylibr |
|
73 |
|
elmapfn |
|
74 |
48 73
|
syl |
|
75 |
|
ssun1 |
|
76 |
75
|
a1i |
|
77 |
|
fnssres |
|
78 |
74 76 77
|
syl2anc |
|
79 |
|
nfv |
|
80 |
|
nfcv |
|
81 |
|
nfcv |
|
82 |
|
nfcv |
|
83 |
|
nfcv |
|
84 |
83
|
nfsum1 |
|
85 |
|
nfcv |
|
86 |
84 85
|
nfeq |
|
87 |
|
nfcv |
|
88 |
86 87
|
nfrabw |
|
89 |
82 88
|
nfmpt |
|
90 |
81 89
|
nfmpt |
|
91 |
1 90
|
nfcxfr |
|
92 |
|
nfcv |
|
93 |
91 92
|
nffv |
|
94 |
|
nfcv |
|
95 |
93 94
|
nffv |
|
96 |
80 95
|
nfel |
|
97 |
79 96
|
nfan |
|
98 |
|
fvres |
|
99 |
98
|
adantl |
|
100 |
9
|
adantr |
|
101 |
58
|
adantr |
|
102 |
12
|
a1i |
|
103 |
50
|
adantr |
|
104 |
76
|
sselda |
|
105 |
103 104
|
ffvelrnd |
|
106 |
102 105
|
sseldd |
|
107 |
100 101 106
|
3jca |
|
108 |
|
elfzle1 |
|
109 |
105 108
|
syl |
|
110 |
7
|
unssad |
|
111 |
|
ssfi |
|
112 |
4 110 111
|
syl2anc |
|
113 |
112
|
ad2antrr |
|
114 |
|
zssre |
|
115 |
12 114
|
sstri |
|
116 |
115
|
a1i |
|
117 |
50
|
adantr |
|
118 |
76
|
sselda |
|
119 |
117 118
|
ffvelrnd |
|
120 |
116 119
|
sseldd |
|
121 |
120
|
adantlr |
|
122 |
|
elfzle1 |
|
123 |
119 122
|
syl |
|
124 |
123
|
adantlr |
|
125 |
|
fveq2 |
|
126 |
|
simpr |
|
127 |
113 121 124 125 126
|
fsumge1 |
|
128 |
112
|
adantr |
|
129 |
120
|
recnd |
|
130 |
128 129
|
fsumcl |
|
131 |
63
|
recnd |
|
132 |
130 131
|
pncand |
|
133 |
|
nfv |
|
134 |
|
nfcv |
|
135 |
5
|
adantr |
|
136 |
6
|
adantr |
|
137 |
|
fveq2 |
|
138 |
133 134 128 135 136 129 137 131
|
fsumsplitsn |
|
139 |
138
|
eqcomd |
|
140 |
125
|
cbvsumv |
|
141 |
140
|
a1i |
|
142 |
42
|
adantr |
|
143 |
47 142
|
eleqtrd |
|
144 |
|
rabid |
|
145 |
143 144
|
sylib |
|
146 |
145
|
simprd |
|
147 |
141 146
|
eqtrd |
|
148 |
139 147
|
eqtrd |
|
149 |
148
|
oveq1d |
|
150 |
132 149
|
eqtr3d |
|
151 |
150
|
adantr |
|
152 |
127 151
|
breqtrd |
|
153 |
107 109 152
|
jca32 |
|
154 |
|
elfz2 |
|
155 |
153 154
|
sylibr |
|
156 |
99 155
|
eqeltrd |
|
157 |
156
|
ex |
|
158 |
97 157
|
ralrimi |
|
159 |
78 158
|
jca |
|
160 |
|
ffnfv |
|
161 |
159 160
|
sylibr |
|
162 |
|
ovexd |
|
163 |
4 110
|
ssexd |
|
164 |
163
|
adantr |
|
165 |
162 164
|
elmapd |
|
166 |
161 165
|
mpbird |
|
167 |
98
|
a1i |
|
168 |
97 167
|
ralrimi |
|
169 |
168
|
sumeq2d |
|
170 |
125
|
cbvsumv |
|
171 |
170
|
eqcomi |
|
172 |
171
|
a1i |
|
173 |
150
|
idi |
|
174 |
169 172 173
|
3eqtrd |
|
175 |
166 174
|
jca |
|
176 |
|
eqidd |
|
177 |
|
simpl |
|
178 |
177
|
fveq1d |
|
179 |
176 178
|
sumeq12rdv |
|
180 |
179
|
eqeq1d |
|
181 |
180
|
elrab |
|
182 |
175 181
|
sylibr |
|
183 |
|
oveq2 |
|
184 |
|
rabeq |
|
185 |
183 184
|
syl |
|
186 |
|
sumeq1 |
|
187 |
186
|
eqeq1d |
|
188 |
187
|
rabbidv |
|
189 |
185 188
|
eqtrd |
|
190 |
189
|
mpteq2dv |
|
191 |
|
elpwg |
|
192 |
163 191
|
syl |
|
193 |
110 192
|
mpbird |
|
194 |
27
|
mptex |
|
195 |
194
|
a1i |
|
196 |
1 190 193 195
|
fvmptd3 |
|
197 |
196
|
adantr |
|
198 |
|
oveq2 |
|
199 |
198
|
oveq1d |
|
200 |
|
rabeq |
|
201 |
199 200
|
syl |
|
202 |
|
eqeq2 |
|
203 |
202
|
rabbidv |
|
204 |
201 203
|
eqtrd |
|
205 |
204
|
cbvmptv |
|
206 |
205
|
a1i |
|
207 |
197 206
|
eqtrd |
|
208 |
|
fveq1 |
|
209 |
208
|
sumeq2sdv |
|
210 |
209
|
eqeq1d |
|
211 |
210
|
cbvrabv |
|
212 |
211
|
a1i |
|
213 |
|
oveq2 |
|
214 |
213
|
oveq1d |
|
215 |
|
rabeq |
|
216 |
214 215
|
syl |
|
217 |
|
eqeq2 |
|
218 |
217
|
rabbidv |
|
219 |
212 216 218
|
3eqtrd |
|
220 |
219
|
adantl |
|
221 |
58 65
|
jca |
|
222 |
|
elnn0z |
|
223 |
221 222
|
sylibr |
|
224 |
|
ovex |
|
225 |
224
|
rabex |
|
226 |
225
|
a1i |
|
227 |
207 220 223 226
|
fvmptd |
|
228 |
227
|
eqcomd |
|
229 |
182 228
|
eleqtrd |
|
230 |
72 229
|
jca |
|
231 |
8 230
|
jca |
|
232 |
|
ovexd |
|
233 |
|
vex |
|
234 |
233
|
resex |
|
235 |
234
|
a1i |
|
236 |
|
opeq12 |
|
237 |
236
|
eqeq2d |
|
238 |
|
eleq1 |
|
239 |
238
|
adantr |
|
240 |
|
simpr |
|
241 |
|
fveq2 |
|
242 |
241
|
adantr |
|
243 |
240 242
|
eleq12d |
|
244 |
239 243
|
anbi12d |
|
245 |
237 244
|
anbi12d |
|
246 |
245
|
spc2egv |
|
247 |
232 235 246
|
syl2anc |
|
248 |
231 247
|
mpd |
|
249 |
|
eliunxp |
|
250 |
248 249
|
sylibr |
|
251 |
250 3
|
fmptd |
|
252 |
95
|
nfcri |
|
253 |
96 252
|
nfan |
|
254 |
79 253
|
nfan |
|
255 |
|
nfv |
|
256 |
254 255
|
nfan |
|
257 |
99
|
eqcomd |
|
258 |
257
|
adantlrr |
|
259 |
258
|
adantlr |
|
260 |
3
|
a1i |
|
261 |
|
opex |
|
262 |
261
|
a1i |
|
263 |
260 262
|
fvmpt2d |
|
264 |
263
|
fveq2d |
|
265 |
264
|
fveq1d |
|
266 |
|
ovex |
|
267 |
266 234
|
op2nd |
|
268 |
267
|
fveq1i |
|
269 |
268
|
a1i |
|
270 |
265 269
|
eqtr2d |
|
271 |
270
|
adantrr |
|
272 |
271
|
ad2antrr |
|
273 |
|
simpr |
|
274 |
|
fveq1 |
|
275 |
274
|
oveq2d |
|
276 |
|
reseq1 |
|
277 |
275 276
|
opeq12d |
|
278 |
|
simpr |
|
279 |
|
opex |
|
280 |
279
|
a1i |
|
281 |
3 277 278 280
|
fvmptd3 |
|
282 |
281
|
adantr |
|
283 |
273 282
|
eqtrd |
|
284 |
283
|
fveq2d |
|
285 |
284
|
adantlrl |
|
286 |
285
|
adantr |
|
287 |
|
ovex |
|
288 |
|
vex |
|
289 |
288
|
resex |
|
290 |
287 289
|
op2nd |
|
291 |
290
|
a1i |
|
292 |
286 291
|
eqtrd |
|
293 |
292
|
fveq1d |
|
294 |
|
fvres |
|
295 |
294
|
adantl |
|
296 |
293 295
|
eqtrd |
|
297 |
259 272 296
|
3eqtrd |
|
298 |
297
|
adantlr |
|
299 |
|
simpl |
|
300 |
|
elunnel1 |
|
301 |
|
elsni |
|
302 |
300 301
|
syl |
|
303 |
302
|
adantll |
|
304 |
|
simpr |
|
305 |
304
|
fveq2d |
|
306 |
2
|
nn0cnd |
|
307 |
306
|
adantr |
|
308 |
307 131
|
nncand |
|
309 |
308
|
eqcomd |
|
310 |
309
|
adantrr |
|
311 |
310
|
adantr |
|
312 |
263
|
fveq2d |
|
313 |
266 234
|
op1st |
|
314 |
313
|
a1i |
|
315 |
312 314
|
eqtr2d |
|
316 |
315
|
oveq2d |
|
317 |
316
|
adantrr |
|
318 |
317
|
adantr |
|
319 |
|
fveq2 |
|
320 |
319
|
adantl |
|
321 |
281
|
fveq2d |
|
322 |
321
|
adantr |
|
323 |
287 289
|
op1st |
|
324 |
323
|
a1i |
|
325 |
320 322 324
|
3eqtrd |
|
326 |
325
|
oveq2d |
|
327 |
306
|
adantr |
|
328 |
|
zsscn |
|
329 |
12 328
|
sstri |
|
330 |
329
|
a1i |
|
331 |
|
eleq1w |
|
332 |
331
|
anbi2d |
|
333 |
|
feq1 |
|
334 |
332 333
|
imbi12d |
|
335 |
334 50
|
chvarvv |
|
336 |
54
|
adantr |
|
337 |
335 336
|
ffvelrnd |
|
338 |
330 337
|
sseldd |
|
339 |
327 338
|
nncand |
|
340 |
339
|
adantr |
|
341 |
|
eqidd |
|
342 |
326 340 341
|
3eqtrd |
|
343 |
342
|
adantlrl |
|
344 |
311 318 343
|
3eqtrd |
|
345 |
344
|
adantr |
|
346 |
|
fveq2 |
|
347 |
346
|
eqcomd |
|
348 |
347
|
adantl |
|
349 |
305 345 348
|
3eqtrd |
|
350 |
349
|
adantlr |
|
351 |
299 303 350
|
syl2anc |
|
352 |
298 351
|
pm2.61dan |
|
353 |
352
|
ex |
|
354 |
256 353
|
ralrimi |
|
355 |
74
|
adantrr |
|
356 |
355
|
adantr |
|
357 |
335
|
ffnd |
|
358 |
357
|
adantrl |
|
359 |
358
|
adantr |
|
360 |
|
eqfnfv |
|
361 |
356 359 360
|
syl2anc |
|
362 |
354 361
|
mpbird |
|
363 |
362
|
ex |
|
364 |
363
|
ralrimivva |
|
365 |
251 364
|
jca |
|
366 |
|
dff13 |
|
367 |
365 366
|
sylibr |
|
368 |
|
eliun |
|
369 |
368
|
biimpi |
|
370 |
369
|
adantl |
|
371 |
|
nfv |
|
372 |
|
nfcv |
|
373 |
|
nfiu1 |
|
374 |
372 373
|
nfel |
|
375 |
371 374
|
nfan |
|
376 |
|
nfv |
|
377 |
|
nfv |
|
378 |
|
nfcv |
|
379 |
|
nfcv |
|
380 |
|
nfcv |
|
381 |
91 380
|
nffv |
|
382 |
|
nfcv |
|
383 |
381 382
|
nffv |
|
384 |
379 383
|
nfxp |
|
385 |
378 384
|
nfel |
|
386 |
79 377 385
|
nf3an |
|
387 |
|
0zd |
|
388 |
10
|
adantr |
|
389 |
388
|
3ad2antl1 |
|
390 |
|
iftrue |
|
391 |
390
|
adantl |
|
392 |
|
fzssz |
|
393 |
392
|
a1i |
|
394 |
|
simp1 |
|
395 |
|
simp2 |
|
396 |
|
xp2nd |
|
397 |
396
|
3ad2ant3 |
|
398 |
196
|
adantr |
|
399 |
|
oveq2 |
|
400 |
399
|
oveq1d |
|
401 |
|
rabeq |
|
402 |
400 401
|
syl |
|
403 |
|
eqeq2 |
|
404 |
403
|
rabbidv |
|
405 |
402 404
|
eqtrd |
|
406 |
405
|
adantl |
|
407 |
|
elfznn0 |
|
408 |
407
|
adantl |
|
409 |
|
ovex |
|
410 |
409
|
rabex |
|
411 |
410
|
a1i |
|
412 |
398 406 408 411
|
fvmptd |
|
413 |
412
|
3adant3 |
|
414 |
397 413
|
eleqtrd |
|
415 |
|
elrabi |
|
416 |
415
|
3ad2ant3 |
|
417 |
394 395 414 416
|
syl3anc |
|
418 |
|
elmapi |
|
419 |
417 418
|
syl |
|
420 |
419
|
adantr |
|
421 |
420
|
ffvelrnda |
|
422 |
393 421
|
sseldd |
|
423 |
391 422
|
eqeltrd |
|
424 |
|
simpl |
|
425 |
302
|
adantll |
|
426 |
|
simpr |
|
427 |
6
|
adantr |
|
428 |
426 427
|
eqneltrd |
|
429 |
428
|
iffalsed |
|
430 |
429
|
3ad2antl1 |
|
431 |
10
|
adantr |
|
432 |
431
|
3ad2antl1 |
|
433 |
|
xp1st |
|
434 |
|
elsni |
|
435 |
433 434
|
syl |
|
436 |
435
|
adantl |
|
437 |
12
|
sseli |
|
438 |
437
|
adantr |
|
439 |
436 438
|
eqeltrd |
|
440 |
439
|
3adant1 |
|
441 |
440
|
adantr |
|
442 |
432 441
|
zsubcld |
|
443 |
430 442
|
eqeltrd |
|
444 |
443
|
adantlr |
|
445 |
424 425 444
|
syl2anc |
|
446 |
423 445
|
pm2.61dan |
|
447 |
387 389 446
|
3jca |
|
448 |
419
|
ffvelrnda |
|
449 |
|
elfzle1 |
|
450 |
448 449
|
syl |
|
451 |
390
|
eqcomd |
|
452 |
451
|
adantl |
|
453 |
450 452
|
breqtrd |
|
454 |
453
|
adantlr |
|
455 |
|
simpll |
|
456 |
|
elfzle2 |
|
457 |
|
elfzel2 |
|
458 |
457
|
zred |
|
459 |
115
|
sseli |
|
460 |
458 459
|
subge0d |
|
461 |
456 460
|
mpbird |
|
462 |
461
|
adantr |
|
463 |
462
|
3ad2antl2 |
|
464 |
394 428
|
sylan |
|
465 |
464
|
iffalsed |
|
466 |
436
|
3adant1 |
|
467 |
466
|
oveq2d |
|
468 |
467
|
adantr |
|
469 |
465 468
|
eqtr2d |
|
470 |
463 469
|
breqtrd |
|
471 |
455 425 470
|
syl2anc |
|
472 |
454 471
|
pm2.61dan |
|
473 |
|
simpl2 |
|
474 |
392
|
sseli |
|
475 |
474
|
zred |
|
476 |
475
|
adantr |
|
477 |
459
|
adantl |
|
478 |
458
|
adantl |
|
479 |
|
elfzle2 |
|
480 |
479
|
adantr |
|
481 |
456
|
adantl |
|
482 |
476 477 478 480 481
|
letrd |
|
483 |
448 473 482
|
syl2anc |
|
484 |
483
|
adantlr |
|
485 |
391 484
|
eqbrtrd |
|
486 |
469
|
eqcomd |
|
487 |
408
|
nn0ge0d |
|
488 |
458
|
adantl |
|
489 |
459
|
adantl |
|
490 |
488 489
|
subge02d |
|
491 |
487 490
|
mpbid |
|
492 |
491
|
adantr |
|
493 |
492
|
3adantl3 |
|
494 |
486 493
|
eqbrtrd |
|
495 |
455 425 494
|
syl2anc |
|
496 |
485 495
|
pm2.61dan |
|
497 |
447 472 496
|
jca32 |
|
498 |
|
elfz2 |
|
499 |
497 498
|
sylibr |
|
500 |
|
eqid |
|
501 |
386 499 500
|
fmptdf |
|
502 |
|
ovexd |
|
503 |
394 23
|
syl |
|
504 |
502 503
|
elmapd |
|
505 |
501 504
|
mpbird |
|
506 |
|
eqidd |
|
507 |
|
eleq1w |
|
508 |
|
fveq2 |
|
509 |
507 508
|
ifbieq1d |
|
510 |
509
|
adantl |
|
511 |
|
simpr |
|
512 |
506 510 511 446
|
fvmptd |
|
513 |
512
|
ex |
|
514 |
386 513
|
ralrimi |
|
515 |
514
|
sumeq2d |
|
516 |
|
nfcv |
|
517 |
394 112
|
syl |
|
518 |
394 5
|
syl |
|
519 |
394 6
|
syl |
|
520 |
390
|
adantl |
|
521 |
448 474
|
syl |
|
522 |
521
|
zcnd |
|
523 |
520 522
|
eqeltrd |
|
524 |
|
eleq1 |
|
525 |
|
fveq2 |
|
526 |
524 525
|
ifbieq1d |
|
527 |
6
|
adantr |
|
528 |
527
|
iffalsed |
|
529 |
528
|
3adant2 |
|
530 |
10
|
3ad2ant1 |
|
531 |
530 440
|
zsubcld |
|
532 |
531
|
zcnd |
|
533 |
529 532
|
eqeltrd |
|
534 |
386 516 517 518 519 523 526 533
|
fsumsplitsn |
|
535 |
390
|
a1i |
|
536 |
386 535
|
ralrimi |
|
537 |
536
|
sumeq2d |
|
538 |
|
eqidd |
|
539 |
|
simpl |
|
540 |
539
|
fveq1d |
|
541 |
538 540
|
sumeq12rdv |
|
542 |
541
|
eqeq1d |
|
543 |
542
|
elrab |
|
544 |
414 543
|
sylib |
|
545 |
544
|
simprd |
|
546 |
537 545
|
eqtrd |
|
547 |
519
|
iffalsed |
|
548 |
547 467
|
eqtrd |
|
549 |
546 548
|
oveq12d |
|
550 |
329
|
sseli |
|
551 |
550
|
3ad2ant2 |
|
552 |
394 306
|
syl |
|
553 |
551 552
|
pncan3d |
|
554 |
549 553
|
eqtrd |
|
555 |
515 534 554
|
3eqtrd |
|
556 |
505 555
|
jca |
|
557 |
|
eleq1w |
|
558 |
|
fveq2 |
|
559 |
557 558
|
ifbieq1d |
|
560 |
559
|
cbvmptv |
|
561 |
560
|
eqeq2i |
|
562 |
561
|
biimpi |
|
563 |
|
fveq1 |
|
564 |
563
|
sumeq2sdv |
|
565 |
562 564
|
syl |
|
566 |
565
|
eqeq1d |
|
567 |
566
|
elrab |
|
568 |
556 567
|
sylibr |
|
569 |
568
|
3exp |
|
570 |
569
|
adantr |
|
571 |
375 376 570
|
rexlimd |
|
572 |
370 571
|
mpd |
|
573 |
42
|
eqcomd |
|
574 |
573
|
adantr |
|
575 |
572 574
|
eleqtrd |
|
576 |
3
|
a1i |
|
577 |
|
simpr |
|
578 |
560
|
a1i |
|
579 |
577 578
|
eqtrd |
|
580 |
|
simpr |
|
581 |
6
|
adantr |
|
582 |
580 581
|
eqneltrd |
|
583 |
582
|
iffalsed |
|
584 |
583
|
adantlr |
|
585 |
54
|
adantr |
|
586 |
|
ovexd |
|
587 |
579 584 585 586
|
fvmptd |
|
588 |
587
|
oveq2d |
|
589 |
588
|
adantlr |
|
590 |
306
|
ad2antrr |
|
591 |
|
nfv |
|
592 |
|
simpl |
|
593 |
|
simpr |
|
594 |
|
simpl |
|
595 |
593 594
|
eqeltrd |
|
596 |
592 436 595
|
syl2anc |
|
597 |
596
|
ex |
|
598 |
597
|
a1i |
|
599 |
374 591 598
|
rexlimd |
|
600 |
369 599
|
mpd |
|
601 |
12
|
sseli |
|
602 |
600 601
|
syl |
|
603 |
602
|
zcnd |
|
604 |
603
|
ad2antlr |
|
605 |
590 604
|
nncand |
|
606 |
589 605
|
eqtrd |
|
607 |
|
reseq1 |
|
608 |
607
|
adantl |
|
609 |
75
|
a1i |
|
610 |
609
|
resmptd |
|
611 |
|
nfv |
|
612 |
390
|
mpteq2ia |
|
613 |
612
|
a1i |
|
614 |
419
|
feqmptd |
|
615 |
613 614
|
eqtr4d |
|
616 |
615
|
3exp |
|
617 |
616
|
adantr |
|
618 |
375 611 617
|
rexlimd |
|
619 |
370 618
|
mpd |
|
620 |
619
|
adantr |
|
621 |
608 610 620
|
3eqtrd |
|
622 |
606 621
|
opeq12d |
|
623 |
|
opex |
|
624 |
623
|
a1i |
|
625 |
576 622 575 624
|
fvmptd |
|
626 |
|
nfv |
|
627 |
|
1st2nd2 |
|
628 |
627
|
eqcomd |
|
629 |
628
|
a1i |
|
630 |
629
|
a1i |
|
631 |
375 626 630
|
rexlimd |
|
632 |
370 631
|
mpd |
|
633 |
625 632
|
eqtr2d |
|
634 |
|
fveq2 |
|
635 |
634
|
rspceeqv |
|
636 |
575 633 635
|
syl2anc |
|
637 |
636
|
ralrimiva |
|
638 |
251 637
|
jca |
|
639 |
|
dffo3 |
|
640 |
638 639
|
sylibr |
|
641 |
367 640
|
jca |
|
642 |
|
df-f1o |
|
643 |
641 642
|
sylibr |
|