Step |
Hyp |
Ref |
Expression |
1 |
|
ftc1anc.g |
|
2 |
|
ftc1anc.a |
|
3 |
|
ftc1anc.b |
|
4 |
|
ftc1anc.le |
|
5 |
|
ftc1anc.s |
|
6 |
|
ftc1anc.d |
|
7 |
|
ftc1anc.i |
|
8 |
|
ftc1anc.f |
|
9 |
1 2 3 4 5 6 7 8
|
ftc1anclem7 |
|
10 |
|
simplll |
|
11 |
|
3simpa |
|
12 |
|
ioossre |
|
13 |
12
|
a1i |
|
14 |
|
rembl |
|
15 |
14
|
a1i |
|
16 |
|
fvex |
|
17 |
|
c0ex |
|
18 |
16 17
|
ifex |
|
19 |
18
|
a1i |
|
20 |
|
eldifn |
|
21 |
20
|
adantl |
|
22 |
21
|
iffalsed |
|
23 |
|
iftrue |
|
24 |
23
|
mpteq2ia |
|
25 |
|
resmpt |
|
26 |
12 25
|
ax-mp |
|
27 |
24 26
|
eqtr4i |
|
28 |
|
i1ff |
|
29 |
28
|
ffvelrnda |
|
30 |
29
|
recnd |
|
31 |
|
ax-icn |
|
32 |
|
i1ff |
|
33 |
32
|
ffvelrnda |
|
34 |
33
|
recnd |
|
35 |
|
mulcl |
|
36 |
31 34 35
|
sylancr |
|
37 |
|
addcl |
|
38 |
30 36 37
|
syl2an |
|
39 |
38
|
anandirs |
|
40 |
|
reex |
|
41 |
40
|
a1i |
|
42 |
29
|
adantlr |
|
43 |
36
|
adantll |
|
44 |
28
|
feqmptd |
|
45 |
44
|
adantr |
|
46 |
40
|
a1i |
|
47 |
31
|
a1i |
|
48 |
|
fconstmpt |
|
49 |
48
|
a1i |
|
50 |
32
|
feqmptd |
|
51 |
46 47 33 49 50
|
offval2 |
|
52 |
51
|
adantl |
|
53 |
41 42 43 45 52
|
offval2 |
|
54 |
|
absf |
|
55 |
54
|
a1i |
|
56 |
55
|
feqmptd |
|
57 |
|
fveq2 |
|
58 |
39 53 56 57
|
fmptco |
|
59 |
|
ftc1anclem3 |
|
60 |
58 59
|
eqeltrrd |
|
61 |
|
i1fmbf |
|
62 |
60 61
|
syl |
|
63 |
|
ioombl |
|
64 |
|
mbfres |
|
65 |
62 63 64
|
sylancl |
|
66 |
27 65
|
eqeltrid |
|
67 |
66
|
adantl |
|
68 |
13 15 19 22 67
|
mbfss |
|
69 |
68
|
adantr |
|
70 |
39
|
abscld |
|
71 |
39
|
absge0d |
|
72 |
|
elrege0 |
|
73 |
70 71 72
|
sylanbrc |
|
74 |
|
0e0icopnf |
|
75 |
|
ifcl |
|
76 |
73 74 75
|
sylancl |
|
77 |
76
|
fmpttd |
|
78 |
77
|
ad2antlr |
|
79 |
70
|
rexrd |
|
80 |
|
elxrge0 |
|
81 |
79 71 80
|
sylanbrc |
|
82 |
|
0e0iccpnf |
|
83 |
|
ifcl |
|
84 |
81 82 83
|
sylancl |
|
85 |
84
|
fmpttd |
|
86 |
85
|
ad2antlr |
|
87 |
|
ifcl |
|
88 |
81 82 87
|
sylancl |
|
89 |
88
|
fmpttd |
|
90 |
|
ffn |
|
91 |
|
frn |
|
92 |
|
ax-resscn |
|
93 |
91 92
|
sstrdi |
|
94 |
|
ffn |
|
95 |
54 94
|
ax-mp |
|
96 |
|
fnco |
|
97 |
95 96
|
mp3an1 |
|
98 |
90 93 97
|
syl2anc |
|
99 |
28 98
|
syl |
|
100 |
99
|
adantr |
|
101 |
|
ffn |
|
102 |
|
frn |
|
103 |
102 92
|
sstrdi |
|
104 |
|
fnco |
|
105 |
95 104
|
mp3an1 |
|
106 |
101 103 105
|
syl2anc |
|
107 |
32 106
|
syl |
|
108 |
107
|
adantl |
|
109 |
|
inidm |
|
110 |
28
|
adantr |
|
111 |
|
fvco3 |
|
112 |
110 111
|
sylan |
|
113 |
32
|
adantl |
|
114 |
|
fvco3 |
|
115 |
113 114
|
sylan |
|
116 |
100 108 41 41 109 112 115
|
offval |
|
117 |
30
|
addid1d |
|
118 |
117
|
mpteq2dva |
|
119 |
40
|
a1i |
|
120 |
17
|
a1i |
|
121 |
31
|
a1i |
|
122 |
48
|
a1i |
|
123 |
|
fconstmpt |
|
124 |
123
|
a1i |
|
125 |
119 121 120 122 124
|
offval2 |
|
126 |
|
it0e0 |
|
127 |
126
|
mpteq2i |
|
128 |
125 127
|
eqtrdi |
|
129 |
119 29 120 44 128
|
offval2 |
|
130 |
118 129 44
|
3eqtr4d |
|
131 |
130
|
coeq2d |
|
132 |
|
i1f0 |
|
133 |
|
ftc1anclem3 |
|
134 |
132 133
|
mpan2 |
|
135 |
131 134
|
eqeltrrd |
|
136 |
135
|
adantr |
|
137 |
|
coeq2 |
|
138 |
137
|
eleq1d |
|
139 |
138 135
|
vtoclga |
|
140 |
139
|
adantl |
|
141 |
136 140
|
i1fadd |
|
142 |
116 141
|
eqeltrrd |
|
143 |
30
|
abscld |
|
144 |
30
|
absge0d |
|
145 |
|
elrege0 |
|
146 |
143 144 145
|
sylanbrc |
|
147 |
34
|
abscld |
|
148 |
34
|
absge0d |
|
149 |
|
elrege0 |
|
150 |
147 148 149
|
sylanbrc |
|
151 |
|
ge0addcl |
|
152 |
146 150 151
|
syl2an |
|
153 |
152
|
anandirs |
|
154 |
153
|
fmpttd |
|
155 |
|
0plef |
|
156 |
154 155
|
sylib |
|
157 |
156
|
simprd |
|
158 |
|
itg2itg1 |
|
159 |
|
itg1cl |
|
160 |
159
|
adantr |
|
161 |
158 160
|
eqeltrd |
|
162 |
142 157 161
|
syl2anc |
|
163 |
|
icossicc |
|
164 |
|
fss |
|
165 |
154 163 164
|
sylancl |
|
166 |
|
0re |
|
167 |
|
ifcl |
|
168 |
70 166 167
|
sylancl |
|
169 |
|
readdcl |
|
170 |
143 147 169
|
syl2an |
|
171 |
170
|
anandirs |
|
172 |
70
|
leidd |
|
173 |
|
breq1 |
|
174 |
|
breq1 |
|
175 |
173 174
|
ifboth |
|
176 |
172 71 175
|
syl2anc |
|
177 |
|
abstri |
|
178 |
30 36 177
|
syl2an |
|
179 |
178
|
anandirs |
|
180 |
|
absmul |
|
181 |
31 34 180
|
sylancr |
|
182 |
|
absi |
|
183 |
182
|
oveq1i |
|
184 |
181 183
|
eqtrdi |
|
185 |
147
|
recnd |
|
186 |
185
|
mulid2d |
|
187 |
184 186
|
eqtrd |
|
188 |
187
|
adantll |
|
189 |
188
|
oveq2d |
|
190 |
179 189
|
breqtrd |
|
191 |
168 70 171 176 190
|
letrd |
|
192 |
191
|
ralrimiva |
|
193 |
|
eqidd |
|
194 |
|
eqidd |
|
195 |
41 168 171 193 194
|
ofrfval2 |
|
196 |
192 195
|
mpbird |
|
197 |
|
itg2le |
|
198 |
89 165 196 197
|
syl3anc |
|
199 |
|
itg2lecl |
|
200 |
89 162 198 199
|
syl3anc |
|
201 |
200
|
ad2antlr |
|
202 |
89
|
ad2antlr |
|
203 |
|
breq1 |
|
204 |
|
breq1 |
|
205 |
|
elioore |
|
206 |
205 172
|
sylan2 |
|
207 |
206
|
adantll |
|
208 |
207
|
adantlr |
|
209 |
2
|
rexrd |
|
210 |
3
|
rexrd |
|
211 |
209 210
|
jca |
|
212 |
|
df-icc |
|
213 |
212
|
elixx3g |
|
214 |
213
|
simprbi |
|
215 |
214
|
simpld |
|
216 |
212
|
elixx3g |
|
217 |
216
|
simprbi |
|
218 |
217
|
simprd |
|
219 |
215 218
|
anim12i |
|
220 |
|
ioossioo |
|
221 |
211 219 220
|
syl2an |
|
222 |
5
|
adantr |
|
223 |
221 222
|
sstrd |
|
224 |
223
|
sselda |
|
225 |
|
iftrue |
|
226 |
224 225
|
syl |
|
227 |
226
|
adantllr |
|
228 |
208 227
|
breqtrrd |
|
229 |
|
breq2 |
|
230 |
|
breq2 |
|
231 |
6
|
sselda |
|
232 |
231
|
adantlr |
|
233 |
71
|
adantll |
|
234 |
232 233
|
syldan |
|
235 |
|
0le0 |
|
236 |
235
|
a1i |
|
237 |
229 230 234 236
|
ifbothda |
|
238 |
237
|
ad2antrr |
|
239 |
203 204 228 238
|
ifbothda |
|
240 |
239
|
ralrimivw |
|
241 |
40
|
a1i |
|
242 |
18
|
a1i |
|
243 |
16 17
|
ifex |
|
244 |
243
|
a1i |
|
245 |
|
eqidd |
|
246 |
|
eqidd |
|
247 |
241 242 244 245 246
|
ofrfval2 |
|
248 |
247
|
ad2antrr |
|
249 |
240 248
|
mpbird |
|
250 |
|
itg2le |
|
251 |
86 202 249 250
|
syl3anc |
|
252 |
|
itg2lecl |
|
253 |
86 201 251 252
|
syl3anc |
|
254 |
8
|
ffvelrnda |
|
255 |
254
|
adantlr |
|
256 |
224 255
|
syldan |
|
257 |
256
|
adantllr |
|
258 |
205 39
|
sylan2 |
|
259 |
258
|
adantll |
|
260 |
259
|
adantlr |
|
261 |
257 260
|
subcld |
|
262 |
261
|
abscld |
|
263 |
261
|
absge0d |
|
264 |
|
elrege0 |
|
265 |
262 263 264
|
sylanbrc |
|
266 |
74
|
a1i |
|
267 |
265 266
|
ifclda |
|
268 |
267
|
adantr |
|
269 |
268
|
fmpttd |
|
270 |
262
|
rexrd |
|
271 |
|
elxrge0 |
|
272 |
270 263 271
|
sylanbrc |
|
273 |
82
|
a1i |
|
274 |
272 273
|
ifclda |
|
275 |
274
|
adantr |
|
276 |
275
|
fmpttd |
|
277 |
|
recncf |
|
278 |
|
prid1g |
|
279 |
277 278
|
ax-mp |
|
280 |
|
ftc1anclem2 |
|
281 |
279 280
|
mp3an3 |
|
282 |
8 7 281
|
syl2anc |
|
283 |
|
imcncf |
|
284 |
|
prid2g |
|
285 |
283 284
|
ax-mp |
|
286 |
|
ftc1anclem2 |
|
287 |
285 286
|
mp3an3 |
|
288 |
8 7 287
|
syl2anc |
|
289 |
282 288
|
readdcld |
|
290 |
289
|
ad2antrr |
|
291 |
201 290
|
readdcld |
|
292 |
|
ge0addcl |
|
293 |
292
|
adantl |
|
294 |
|
ifcl |
|
295 |
73 74 294
|
sylancl |
|
296 |
295
|
fmpttd |
|
297 |
296
|
adantl |
|
298 |
292
|
adantl |
|
299 |
254
|
recld |
|
300 |
299
|
recnd |
|
301 |
300
|
abscld |
|
302 |
300
|
absge0d |
|
303 |
|
elrege0 |
|
304 |
301 302 303
|
sylanbrc |
|
305 |
74
|
a1i |
|
306 |
304 305
|
ifclda |
|
307 |
306
|
adantr |
|
308 |
307
|
fmpttd |
|
309 |
254
|
imcld |
|
310 |
309
|
recnd |
|
311 |
310
|
abscld |
|
312 |
310
|
absge0d |
|
313 |
|
elrege0 |
|
314 |
311 312 313
|
sylanbrc |
|
315 |
314 305
|
ifclda |
|
316 |
315
|
adantr |
|
317 |
316
|
fmpttd |
|
318 |
298 308 317 241 241 109
|
off |
|
319 |
318
|
adantr |
|
320 |
40
|
a1i |
|
321 |
293 297 319 320 320 109
|
off |
|
322 |
|
fss |
|
323 |
321 163 322
|
sylancl |
|
324 |
323
|
adantr |
|
325 |
|
0xr |
|
326 |
325
|
a1i |
|
327 |
270 326
|
ifclda |
|
328 |
254
|
adantlr |
|
329 |
39
|
adantll |
|
330 |
232 329
|
syldan |
|
331 |
328 330
|
subcld |
|
332 |
331
|
abscld |
|
333 |
332
|
rexrd |
|
334 |
325
|
a1i |
|
335 |
333 334
|
ifclda |
|
336 |
335
|
adantr |
|
337 |
330
|
abscld |
|
338 |
|
0red |
|
339 |
337 338
|
ifclda |
|
340 |
|
0red |
|
341 |
301 340
|
ifclda |
|
342 |
311 340
|
ifclda |
|
343 |
341 342
|
readdcld |
|
344 |
343
|
adantr |
|
345 |
339 344
|
readdcld |
|
346 |
345
|
rexrd |
|
347 |
346
|
adantr |
|
348 |
|
breq1 |
|
349 |
|
breq1 |
|
350 |
224
|
adantllr |
|
351 |
332
|
leidd |
|
352 |
351
|
adantlr |
|
353 |
|
iftrue |
|
354 |
353
|
adantl |
|
355 |
352 354
|
breqtrrd |
|
356 |
350 355
|
syldan |
|
357 |
|
breq2 |
|
358 |
|
breq2 |
|
359 |
331
|
absge0d |
|
360 |
357 358 359 236
|
ifbothda |
|
361 |
360
|
ad2antrr |
|
362 |
348 349 356 361
|
ifbothda |
|
363 |
254
|
negcld |
|
364 |
363
|
adantlr |
|
365 |
330 364
|
addcld |
|
366 |
365
|
abscld |
|
367 |
363
|
abscld |
|
368 |
367
|
adantlr |
|
369 |
337 368
|
readdcld |
|
370 |
301 311
|
readdcld |
|
371 |
370
|
adantlr |
|
372 |
337 371
|
readdcld |
|
373 |
330 364
|
abstrid |
|
374 |
|
mulcl |
|
375 |
31 310 374
|
sylancr |
|
376 |
300 375
|
abstrid |
|
377 |
254
|
absnegd |
|
378 |
254
|
replimd |
|
379 |
378
|
fveq2d |
|
380 |
377 379
|
eqtrd |
|
381 |
|
absmul |
|
382 |
31 310 381
|
sylancr |
|
383 |
182
|
oveq1i |
|
384 |
382 383
|
eqtrdi |
|
385 |
311
|
recnd |
|
386 |
385
|
mulid2d |
|
387 |
384 386
|
eqtr2d |
|
388 |
387
|
oveq2d |
|
389 |
376 380 388
|
3brtr4d |
|
390 |
389
|
adantlr |
|
391 |
368 371 337 390
|
leadd2dd |
|
392 |
366 369 372 373 391
|
letrd |
|
393 |
328 330
|
abssubd |
|
394 |
353
|
adantl |
|
395 |
330 328
|
negsubd |
|
396 |
395
|
fveq2d |
|
397 |
393 394 396
|
3eqtr4d |
|
398 |
|
iftrue |
|
399 |
398
|
adantl |
|
400 |
392 397 399
|
3brtr4d |
|
401 |
400
|
ex |
|
402 |
235
|
a1i |
|
403 |
|
iffalse |
|
404 |
|
iffalse |
|
405 |
402 403 404
|
3brtr4d |
|
406 |
401 405
|
pm2.61d1 |
|
407 |
|
iftrue |
|
408 |
|
iftrue |
|
409 |
407 408
|
oveq12d |
|
410 |
225 409
|
oveq12d |
|
411 |
410 398
|
eqtr4d |
|
412 |
|
00id |
|
413 |
412
|
oveq2i |
|
414 |
413 412
|
eqtri |
|
415 |
|
iffalse |
|
416 |
|
iffalse |
|
417 |
|
iffalse |
|
418 |
416 417
|
oveq12d |
|
419 |
415 418
|
oveq12d |
|
420 |
414 419 404
|
3eqtr4a |
|
421 |
411 420
|
pm2.61i |
|
422 |
406 421
|
breqtrrdi |
|
423 |
422
|
adantr |
|
424 |
327 336 347 362 423
|
xrletrd |
|
425 |
424
|
ralrimivw |
|
426 |
|
fvex |
|
427 |
426 17
|
ifex |
|
428 |
427
|
a1i |
|
429 |
|
ovexd |
|
430 |
|
eqidd |
|
431 |
|
ovexd |
|
432 |
341
|
adantr |
|
433 |
342
|
adantr |
|
434 |
|
eqidd |
|
435 |
|
eqidd |
|
436 |
241 432 433 434 435
|
offval2 |
|
437 |
241 244 431 246 436
|
offval2 |
|
438 |
241 428 429 430 437
|
ofrfval2 |
|
439 |
438
|
ad2antrr |
|
440 |
425 439
|
mpbird |
|
441 |
|
itg2le |
|
442 |
276 324 440 441
|
syl3anc |
|
443 |
6
|
adantr |
|
444 |
243
|
a1i |
|
445 |
|
eldifn |
|
446 |
445
|
iffalsed |
|
447 |
446
|
adantl |
|
448 |
|
ovexd |
|
449 |
41 42 448 45 52
|
offval2 |
|
450 |
39 449 56 57
|
fmptco |
|
451 |
450
|
reseq1d |
|
452 |
6
|
resmptd |
|
453 |
451 452
|
sylan9eqr |
|
454 |
225
|
mpteq2ia |
|
455 |
453 454
|
eqtr4di |
|
456 |
|
i1fmbf |
|
457 |
59 456
|
syl |
|
458 |
8
|
fdmd |
|
459 |
|
iblmbf |
|
460 |
|
mbfdm |
|
461 |
7 459 460
|
3syl |
|
462 |
458 461
|
eqeltrrd |
|
463 |
|
mbfres |
|
464 |
457 462 463
|
syl2anr |
|
465 |
455 464
|
eqeltrrd |
|
466 |
443 15 444 447 465
|
mbfss |
|
467 |
200
|
adantl |
|
468 |
|
0cnd |
|
469 |
300 468
|
ifclda |
|
470 |
469
|
adantr |
|
471 |
|
eqidd |
|
472 |
54
|
a1i |
|
473 |
472
|
feqmptd |
|
474 |
|
fveq2 |
|
475 |
|
fvif |
|
476 |
|
abs0 |
|
477 |
|
ifeq2 |
|
478 |
476 477
|
ax-mp |
|
479 |
475 478
|
eqtri |
|
480 |
474 479
|
eqtrdi |
|
481 |
470 471 473 480
|
fmptco |
|
482 |
299 340
|
ifclda |
|
483 |
482
|
adantr |
|
484 |
483
|
fmpttd |
|
485 |
14
|
a1i |
|
486 |
482
|
adantr |
|
487 |
445
|
adantl |
|
488 |
487
|
iffalsed |
|
489 |
|
iftrue |
|
490 |
489
|
mpteq2ia |
|
491 |
8
|
feqmptd |
|
492 |
7 459
|
syl |
|
493 |
491 492
|
eqeltrrd |
|
494 |
254
|
ismbfcn2 |
|
495 |
493 494
|
mpbid |
|
496 |
495
|
simpld |
|
497 |
490 496
|
eqeltrid |
|
498 |
6 485 486 488 497
|
mbfss |
|
499 |
|
ftc1anclem1 |
|
500 |
484 498 499
|
syl2anc |
|
501 |
481 500
|
eqeltrrd |
|
502 |
501 308 282 317 288
|
itg2addnc |
|
503 |
502 289
|
eqeltrd |
|
504 |
503
|
adantr |
|
505 |
466 297 467 319 504
|
itg2addnc |
|
506 |
502
|
adantr |
|
507 |
506
|
oveq2d |
|
508 |
505 507
|
eqtrd |
|
509 |
508
|
adantr |
|
510 |
442 509
|
breqtrd |
|
511 |
|
itg2lecl |
|
512 |
276 291 510 511
|
syl3anc |
|
513 |
69 78 253 269 512
|
itg2addnc |
|
514 |
241 242 428 245 430
|
offval2 |
|
515 |
|
eqeq2 |
|
516 |
|
eqeq2 |
|
517 |
|
iftrue |
|
518 |
23 517
|
oveq12d |
|
519 |
518
|
adantl |
|
520 |
|
iffalse |
|
521 |
|
iffalse |
|
522 |
520 521
|
oveq12d |
|
523 |
522 412
|
eqtrdi |
|
524 |
523
|
adantl |
|
525 |
515 516 519 524
|
ifbothda |
|
526 |
525
|
mpteq2dv |
|
527 |
514 526
|
eqtrd |
|
528 |
527
|
ad2antrr |
|
529 |
|
simplr |
|
530 |
258
|
abscld |
|
531 |
530
|
recnd |
|
532 |
529 531
|
sylan |
|
533 |
262
|
recnd |
|
534 |
532 533
|
addcomd |
|
535 |
534
|
ifeq1da |
|
536 |
535
|
mpteq2dv |
|
537 |
528 536
|
eqtrd |
|
538 |
537
|
fveq2d |
|
539 |
513 538
|
eqtr3d |
|
540 |
10 11 539
|
syl2an |
|
541 |
540
|
adantr |
|
542 |
|
rpcn |
|
543 |
542
|
2halvesd |
|
544 |
543
|
ad3antlr |
|
545 |
9 541 544
|
3brtr3d |
|