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 |
|
rphalfcl |
|
10 |
1 2 3 4 5 6 7 8
|
ftc1anclem5 |
|
11 |
9 10
|
sylan2 |
|
12 |
|
eqid |
|
13 |
|
ax-icn |
|
14 |
|
ine0 |
|
15 |
13 14
|
reccli |
|
16 |
15
|
a1i |
|
17 |
8
|
ffvelrnda |
|
18 |
8
|
feqmptd |
|
19 |
18 7
|
eqeltrrd |
|
20 |
|
divrec2 |
|
21 |
13 14 20
|
mp3an23 |
|
22 |
17 21
|
syl |
|
23 |
22
|
mpteq2dva |
|
24 |
|
iblmbf |
|
25 |
19 24
|
syl |
|
26 |
|
2fveq3 |
|
27 |
26
|
cbvmptv |
|
28 |
27
|
eleq1i |
|
29 |
17
|
recld |
|
30 |
29
|
recnd |
|
31 |
30
|
adantlr |
|
32 |
28
|
biimpri |
|
33 |
32
|
adantl |
|
34 |
31 33
|
mbfneg |
|
35 |
28 34
|
sylan2b |
|
36 |
8
|
ffvelrnda |
|
37 |
36
|
recld |
|
38 |
37
|
recnd |
|
39 |
38
|
negnegd |
|
40 |
39
|
mpteq2dva |
|
41 |
40 27
|
eqtr4di |
|
42 |
41
|
adantr |
|
43 |
|
negex |
|
44 |
43
|
a1i |
|
45 |
26
|
negeqd |
|
46 |
45
|
cbvmptv |
|
47 |
46
|
eleq1i |
|
48 |
47
|
biimpi |
|
49 |
48
|
adantl |
|
50 |
44 49
|
mbfneg |
|
51 |
42 50
|
eqeltrrd |
|
52 |
35 51
|
impbida |
|
53 |
|
divcl |
|
54 |
|
imre |
|
55 |
53 54
|
syl |
|
56 |
13 14 55
|
mp3an23 |
|
57 |
13 14 53
|
mp3an23 |
|
58 |
|
mulneg1 |
|
59 |
13 57 58
|
sylancr |
|
60 |
|
divcan2 |
|
61 |
13 14 60
|
mp3an23 |
|
62 |
61
|
negeqd |
|
63 |
59 62
|
eqtrd |
|
64 |
63
|
fveq2d |
|
65 |
|
reneg |
|
66 |
56 64 65
|
3eqtrd |
|
67 |
17 66
|
syl |
|
68 |
67
|
mpteq2dva |
|
69 |
68
|
eleq1d |
|
70 |
52 69
|
bitr4d |
|
71 |
|
imval |
|
72 |
17 71
|
syl |
|
73 |
72
|
mpteq2dva |
|
74 |
73
|
eleq1d |
|
75 |
70 74
|
anbi12d |
|
76 |
|
ancom |
|
77 |
75 76
|
bitrdi |
|
78 |
17
|
ismbfcn2 |
|
79 |
17 57
|
syl |
|
80 |
79
|
ismbfcn2 |
|
81 |
77 78 80
|
3bitr4d |
|
82 |
25 81
|
mpbid |
|
83 |
23 82
|
eqeltrrd |
|
84 |
16 17 19 83
|
iblmulc2nc |
|
85 |
|
mulcl |
|
86 |
15 17 85
|
sylancr |
|
87 |
86
|
fmpttd |
|
88 |
12 2 3 4 5 6 84 87
|
ftc1anclem5 |
|
89 |
9 88
|
sylan2 |
|
90 |
8
|
ffvelrnda |
|
91 |
|
0cnd |
|
92 |
90 91
|
ifclda |
|
93 |
|
imval |
|
94 |
92 93
|
syl |
|
95 |
|
fveq2 |
|
96 |
95
|
oveq2d |
|
97 |
|
eqid |
|
98 |
|
ovex |
|
99 |
96 97 98
|
fvmpt |
|
100 |
99
|
adantl |
|
101 |
|
divrec2 |
|
102 |
13 14 101
|
mp3an23 |
|
103 |
90 102
|
syl |
|
104 |
100 103
|
eqtr4d |
|
105 |
104
|
ifeq1da |
|
106 |
|
ovif |
|
107 |
13 14
|
div0i |
|
108 |
|
ifeq2 |
|
109 |
107 108
|
ax-mp |
|
110 |
106 109
|
eqtri |
|
111 |
105 110
|
eqtr4di |
|
112 |
111
|
fveq2d |
|
113 |
94 112
|
eqtr4d |
|
114 |
113
|
fvoveq1d |
|
115 |
114
|
mpteq2dv |
|
116 |
115
|
fveq2d |
|
117 |
116
|
breq1d |
|
118 |
117
|
rexbidv |
|
119 |
118
|
adantr |
|
120 |
89 119
|
mpbird |
|
121 |
|
reeanv |
|
122 |
|
eleq1w |
|
123 |
|
fveq2 |
|
124 |
122 123
|
ifbieq1d |
|
125 |
124
|
fveq2d |
|
126 |
|
eqid |
|
127 |
|
fvex |
|
128 |
125 126 127
|
fvmpt |
|
129 |
128
|
fvoveq1d |
|
130 |
129
|
mpteq2ia |
|
131 |
130
|
fveq2i |
|
132 |
|
rembl |
|
133 |
132
|
a1i |
|
134 |
|
0cnd |
|
135 |
36 134
|
ifclda |
|
136 |
135
|
adantr |
|
137 |
|
eldifn |
|
138 |
137
|
adantl |
|
139 |
138
|
iffalsed |
|
140 |
8
|
feqmptd |
|
141 |
|
iftrue |
|
142 |
141
|
mpteq2ia |
|
143 |
140 142
|
eqtr4di |
|
144 |
143 7
|
eqeltrrd |
|
145 |
6 133 136 139 144
|
iblss2 |
|
146 |
135
|
adantr |
|
147 |
146
|
iblcn |
|
148 |
145 147
|
mpbid |
|
149 |
148
|
simpld |
|
150 |
146
|
recld |
|
151 |
150
|
fmpttd |
|
152 |
149 151
|
jca |
|
153 |
|
ftc1anclem4 |
|
154 |
153
|
3expb |
|
155 |
152 154
|
sylan2 |
|
156 |
155
|
ancoms |
|
157 |
131 156
|
eqeltrrid |
|
158 |
124
|
fveq2d |
|
159 |
|
eqid |
|
160 |
|
fvex |
|
161 |
158 159 160
|
fvmpt |
|
162 |
161
|
fvoveq1d |
|
163 |
162
|
mpteq2ia |
|
164 |
163
|
fveq2i |
|
165 |
148
|
simprd |
|
166 |
135
|
imcld |
|
167 |
166
|
adantr |
|
168 |
167
|
fmpttd |
|
169 |
165 168
|
jca |
|
170 |
|
ftc1anclem4 |
|
171 |
170
|
3expb |
|
172 |
169 171
|
sylan2 |
|
173 |
172
|
ancoms |
|
174 |
164 173
|
eqeltrrid |
|
175 |
157 174
|
anim12dan |
|
176 |
9
|
rpred |
|
177 |
176 176
|
jca |
|
178 |
|
lt2add |
|
179 |
175 177 178
|
syl2an |
|
180 |
179
|
an32s |
|
181 |
92
|
recld |
|
182 |
181
|
recnd |
|
183 |
|
i1ff |
|
184 |
183
|
ffvelrnda |
|
185 |
184
|
recnd |
|
186 |
|
subcl |
|
187 |
182 185 186
|
syl2an |
|
188 |
187
|
anassrs |
|
189 |
188
|
adantlrr |
|
190 |
92
|
imcld |
|
191 |
190
|
recnd |
|
192 |
|
i1ff |
|
193 |
192
|
ffvelrnda |
|
194 |
193
|
recnd |
|
195 |
|
subcl |
|
196 |
191 194 195
|
syl2an |
|
197 |
196
|
anassrs |
|
198 |
|
mulcl |
|
199 |
13 197 198
|
sylancr |
|
200 |
199
|
adantlrl |
|
201 |
189 200
|
addcld |
|
202 |
201
|
abscld |
|
203 |
202
|
rexrd |
|
204 |
201
|
absge0d |
|
205 |
|
elxrge0 |
|
206 |
203 204 205
|
sylanbrc |
|
207 |
206
|
fmpttd |
|
208 |
|
icossicc |
|
209 |
|
ge0addcl |
|
210 |
208 209
|
sselid |
|
211 |
210
|
adantl |
|
212 |
188
|
abscld |
|
213 |
188
|
absge0d |
|
214 |
|
elrege0 |
|
215 |
212 213 214
|
sylanbrc |
|
216 |
215
|
fmpttd |
|
217 |
216
|
adantrr |
|
218 |
197
|
abscld |
|
219 |
197
|
absge0d |
|
220 |
|
elrege0 |
|
221 |
218 219 220
|
sylanbrc |
|
222 |
221
|
fmpttd |
|
223 |
222
|
adantrl |
|
224 |
|
reex |
|
225 |
224
|
a1i |
|
226 |
|
inidm |
|
227 |
211 217 223 225 225 226
|
off |
|
228 |
189 200
|
abstrid |
|
229 |
228
|
ralrimiva |
|
230 |
|
ovexd |
|
231 |
|
eqidd |
|
232 |
|
fvexd |
|
233 |
|
fvexd |
|
234 |
|
eqidd |
|
235 |
|
absmul |
|
236 |
13 197 235
|
sylancr |
|
237 |
|
absi |
|
238 |
237
|
oveq1i |
|
239 |
218
|
recnd |
|
240 |
239
|
mulid2d |
|
241 |
238 240
|
syl5eq |
|
242 |
236 241
|
eqtr2d |
|
243 |
242
|
mpteq2dva |
|
244 |
243
|
adantrl |
|
245 |
225 232 233 234 244
|
offval2 |
|
246 |
225 202 230 231 245
|
ofrfval2 |
|
247 |
229 246
|
mpbird |
|
248 |
|
itg2le |
|
249 |
207 227 247 248
|
syl3anc |
|
250 |
|
absf |
|
251 |
250
|
a1i |
|
252 |
251 188
|
cofmpt |
|
253 |
|
resubcl |
|
254 |
181 184 253
|
syl2an |
|
255 |
254
|
anassrs |
|
256 |
255
|
fmpttd |
|
257 |
132
|
a1i |
|
258 |
|
iunin2 |
|
259 |
|
imaiun |
|
260 |
|
iunid |
|
261 |
260
|
imaeq2i |
|
262 |
259 261
|
eqtr3i |
|
263 |
262
|
ineq2i |
|
264 |
258 263
|
eqtri |
|
265 |
|
cnvimass |
|
266 |
|
ovex |
|
267 |
|
eqid |
|
268 |
266 267
|
dmmpti |
|
269 |
265 268
|
sseqtri |
|
270 |
|
cnvimarndm |
|
271 |
183
|
fdmd |
|
272 |
270 271
|
syl5eq |
|
273 |
269 272
|
sseqtrrid |
|
274 |
|
df-ss |
|
275 |
273 274
|
sylib |
|
276 |
264 275
|
syl5eq |
|
277 |
276
|
ad2antlr |
|
278 |
183
|
frnd |
|
279 |
278
|
ad2antlr |
|
280 |
279
|
sselda |
|
281 |
181
|
ad2antrr |
|
282 |
|
resubcl |
|
283 |
181 282
|
sylan |
|
284 |
283
|
adantlr |
|
285 |
281 284
|
2thd |
|
286 |
|
ltaddsub |
|
287 |
181 286
|
syl3an3 |
|
288 |
287
|
3comr |
|
289 |
288
|
3expa |
|
290 |
285 289
|
anbi12d |
|
291 |
|
readdcl |
|
292 |
291
|
rexrd |
|
293 |
292
|
adantll |
|
294 |
|
elioopnf |
|
295 |
293 294
|
syl |
|
296 |
|
rexr |
|
297 |
296
|
ad2antlr |
|
298 |
|
elioopnf |
|
299 |
297 298
|
syl |
|
300 |
290 295 299
|
3bitr4rd |
|
301 |
|
oveq2 |
|
302 |
301
|
eleq1d |
|
303 |
302
|
bibi1d |
|
304 |
300 303
|
syl5ibrcom |
|
305 |
304
|
pm5.32rd |
|
306 |
305
|
adantllr |
|
307 |
280 306
|
syldan |
|
308 |
307
|
rabbidv |
|
309 |
183
|
feqmptd |
|
310 |
309
|
cnveqd |
|
311 |
310
|
imaeq1d |
|
312 |
311
|
ineq2d |
|
313 |
267
|
mptpreima |
|
314 |
|
vex |
|
315 |
|
eqid |
|
316 |
315
|
mptiniseg |
|
317 |
314 316
|
ax-mp |
|
318 |
313 317
|
ineq12i |
|
319 |
|
inrab |
|
320 |
318 319
|
eqtri |
|
321 |
312 320
|
eqtrdi |
|
322 |
321
|
ad3antlr |
|
323 |
311
|
ineq2d |
|
324 |
|
eqid |
|
325 |
324
|
mptpreima |
|
326 |
325 317
|
ineq12i |
|
327 |
|
inrab |
|
328 |
326 327
|
eqtri |
|
329 |
323 328
|
eqtrdi |
|
330 |
329
|
ad3antlr |
|
331 |
308 322 330
|
3eqtr4d |
|
332 |
331
|
iuneq2dv |
|
333 |
277 332
|
eqtr3d |
|
334 |
|
i1frn |
|
335 |
334
|
adantl |
|
336 |
92
|
adantr |
|
337 |
|
eldifn |
|
338 |
337
|
adantl |
|
339 |
338
|
iffalsed |
|
340 |
8
|
feqmptd |
|
341 |
|
iftrue |
|
342 |
341
|
mpteq2ia |
|
343 |
340 342
|
eqtr4di |
|
344 |
|
iblmbf |
|
345 |
7 344
|
syl |
|
346 |
343 345
|
eqeltrrd |
|
347 |
6 133 336 339 346
|
mbfss |
|
348 |
92
|
adantr |
|
349 |
348
|
ismbfcn2 |
|
350 |
347 349
|
mpbid |
|
351 |
350
|
simpld |
|
352 |
181
|
adantr |
|
353 |
352
|
fmpttd |
|
354 |
|
mbfima |
|
355 |
351 353 354
|
syl2anc |
|
356 |
|
i1fima |
|
357 |
|
inmbl |
|
358 |
355 356 357
|
syl2an |
|
359 |
358
|
ralrimivw |
|
360 |
|
finiunmbl |
|
361 |
335 359 360
|
syl2anc |
|
362 |
361
|
adantr |
|
363 |
333 362
|
eqeltrd |
|
364 |
|
iunin2 |
|
365 |
262
|
ineq2i |
|
366 |
364 365
|
eqtri |
|
367 |
|
cnvimass |
|
368 |
367 268
|
sseqtri |
|
369 |
368 272
|
sseqtrrid |
|
370 |
|
df-ss |
|
371 |
369 370
|
sylib |
|
372 |
366 371
|
syl5eq |
|
373 |
372
|
ad2antlr |
|
374 |
284 281
|
2thd |
|
375 |
|
ltsubadd |
|
376 |
181 375
|
syl3an1 |
|
377 |
376
|
3expa |
|
378 |
377
|
an32s |
|
379 |
374 378
|
anbi12d |
|
380 |
|
elioomnf |
|
381 |
297 380
|
syl |
|
382 |
|
elioomnf |
|
383 |
293 382
|
syl |
|
384 |
379 381 383
|
3bitr4d |
|
385 |
301
|
eleq1d |
|
386 |
385
|
bibi1d |
|
387 |
384 386
|
syl5ibrcom |
|
388 |
387
|
pm5.32rd |
|
389 |
388
|
adantllr |
|
390 |
280 389
|
syldan |
|
391 |
390
|
rabbidv |
|
392 |
311
|
ineq2d |
|
393 |
267
|
mptpreima |
|
394 |
393 317
|
ineq12i |
|
395 |
|
inrab |
|
396 |
394 395
|
eqtri |
|
397 |
392 396
|
eqtrdi |
|
398 |
397
|
ad3antlr |
|
399 |
311
|
ineq2d |
|
400 |
324
|
mptpreima |
|
401 |
400 317
|
ineq12i |
|
402 |
|
inrab |
|
403 |
401 402
|
eqtri |
|
404 |
399 403
|
eqtrdi |
|
405 |
404
|
ad3antlr |
|
406 |
391 398 405
|
3eqtr4d |
|
407 |
406
|
iuneq2dv |
|
408 |
373 407
|
eqtr3d |
|
409 |
|
mbfima |
|
410 |
351 353 409
|
syl2anc |
|
411 |
|
inmbl |
|
412 |
410 356 411
|
syl2an |
|
413 |
412
|
ralrimivw |
|
414 |
|
finiunmbl |
|
415 |
335 413 414
|
syl2anc |
|
416 |
415
|
adantr |
|
417 |
408 416
|
eqeltrd |
|
418 |
256 257 363 417
|
ismbf2d |
|
419 |
|
ftc1anclem1 |
|
420 |
256 418 419
|
syl2anc |
|
421 |
252 420
|
eqeltrrd |
|
422 |
421
|
adantrr |
|
423 |
157
|
adantrr |
|
424 |
174
|
adantrl |
|
425 |
422 217 423 223 424
|
itg2addnc |
|
426 |
249 425
|
breqtrd |
|
427 |
426
|
adantlr |
|
428 |
|
itg2cl |
|
429 |
207 428
|
syl |
|
430 |
429
|
adantlr |
|
431 |
|
readdcl |
|
432 |
157 174 431
|
syl2an |
|
433 |
432
|
anandis |
|
434 |
433
|
rexrd |
|
435 |
434
|
adantlr |
|
436 |
9 9
|
rpaddcld |
|
437 |
436
|
rpxrd |
|
438 |
437
|
ad2antlr |
|
439 |
|
xrlelttr |
|
440 |
430 435 438 439
|
syl3anc |
|
441 |
427 440
|
mpand |
|
442 |
180 441
|
syld |
|
443 |
|
mulcl |
|
444 |
13 191 443
|
sylancr |
|
445 |
182 444
|
jca |
|
446 |
|
mulcl |
|
447 |
13 194 446
|
sylancr |
|
448 |
185 447
|
anim12i |
|
449 |
448
|
anandirs |
|
450 |
|
addsub4 |
|
451 |
445 449 450
|
syl2an |
|
452 |
451
|
anassrs |
|
453 |
92
|
replimd |
|
454 |
453
|
ad2antrr |
|
455 |
454
|
oveq1d |
|
456 |
194
|
adantll |
|
457 |
|
subdi |
|
458 |
13 191 456 457
|
mp3an3an |
|
459 |
458
|
anassrs |
|
460 |
459
|
oveq2d |
|
461 |
452 455 460
|
3eqtr4rd |
|
462 |
461
|
fveq2d |
|
463 |
462
|
mpteq2dva |
|
464 |
463
|
fveq2d |
|
465 |
464
|
adantlr |
|
466 |
|
rpcn |
|
467 |
466
|
2halvesd |
|
468 |
467
|
ad2antlr |
|
469 |
465 468
|
breq12d |
|
470 |
442 469
|
sylibd |
|
471 |
470
|
reximdvva |
|
472 |
121 471
|
syl5bir |
|
473 |
11 120 472
|
mp2and |
|