Step |
Hyp |
Ref |
Expression |
1 |
|
itg2addnc.f1 |
|
2 |
|
itg2addnc.f2 |
|
3 |
|
rge0ssre |
|
4 |
|
fss |
|
5 |
2 3 4
|
sylancl |
|
6 |
5
|
ad2antrr |
|
7 |
6
|
ffvelrnda |
|
8 |
|
rpre |
|
9 |
|
3re |
|
10 |
|
3ne0 |
|
11 |
9 10
|
pm3.2i |
|
12 |
|
redivcl |
|
13 |
12
|
3expb |
|
14 |
8 11 13
|
sylancl |
|
15 |
14
|
ad2antlr |
|
16 |
|
rpcnne0 |
|
17 |
|
3cn |
|
18 |
17 10
|
pm3.2i |
|
19 |
|
divne0 |
|
20 |
16 18 19
|
sylancl |
|
21 |
20
|
ad2antlr |
|
22 |
7 15 21
|
redivcld |
|
23 |
|
reflcl |
|
24 |
22 23
|
syl |
|
25 |
|
peano2rem |
|
26 |
24 25
|
syl |
|
27 |
26 15
|
remulcld |
|
28 |
|
i1ff |
|
29 |
28
|
ad2antlr |
|
30 |
29
|
ffvelrnda |
|
31 |
27 30
|
ifcld |
|
32 |
31
|
fmpttd |
|
33 |
|
fzfi |
|
34 |
|
ovex |
|
35 |
|
eqid |
|
36 |
34 35
|
fnmpti |
|
37 |
|
dffn4 |
|
38 |
36 37
|
mpbi |
|
39 |
|
fofi |
|
40 |
33 38 39
|
mp2an |
|
41 |
|
i1frn |
|
42 |
41
|
ad2antlr |
|
43 |
|
unfi |
|
44 |
40 42 43
|
sylancr |
|
45 |
|
0zd |
|
46 |
28
|
frnd |
|
47 |
|
i1f0rn |
|
48 |
|
elex2 |
|
49 |
47 48
|
syl |
|
50 |
|
n0 |
|
51 |
49 50
|
sylibr |
|
52 |
|
fimaxre2 |
|
53 |
46 41 52
|
syl2anc |
|
54 |
|
suprcl |
|
55 |
46 51 53 54
|
syl3anc |
|
56 |
55
|
ad3antlr |
|
57 |
56 15 21
|
redivcld |
|
58 |
|
peano2re |
|
59 |
57 58
|
syl |
|
60 |
|
ceicl |
|
61 |
59 60
|
syl |
|
62 |
61
|
adantr |
|
63 |
22
|
flcld |
|
64 |
63
|
adantr |
|
65 |
|
3nn |
|
66 |
|
nnrp |
|
67 |
65 66
|
ax-mp |
|
68 |
|
rpdivcl |
|
69 |
67 68
|
mpan2 |
|
70 |
69
|
ad2antlr |
|
71 |
2
|
ad2antrr |
|
72 |
71
|
ffvelrnda |
|
73 |
|
elrege0 |
|
74 |
72 73
|
sylib |
|
75 |
74
|
simprd |
|
76 |
7 70 75
|
divge0d |
|
77 |
|
flge0nn0 |
|
78 |
22 76 77
|
syl2anc |
|
79 |
78
|
nn0ge0d |
|
80 |
79
|
adantr |
|
81 |
46 51 53
|
3jca |
|
82 |
81
|
ad3antlr |
|
83 |
|
ffn |
|
84 |
28 83
|
syl |
|
85 |
|
dffn3 |
|
86 |
84 85
|
sylib |
|
87 |
86
|
ad2antlr |
|
88 |
87
|
ffvelrnda |
|
89 |
|
suprub |
|
90 |
82 88 89
|
syl2anc |
|
91 |
|
letr |
|
92 |
27 30 56 91
|
syl3anc |
|
93 |
26 56 70
|
lemuldivd |
|
94 |
|
1red |
|
95 |
24 94 57
|
lesubaddd |
|
96 |
93 95
|
bitrd |
|
97 |
|
ceige |
|
98 |
59 97
|
syl |
|
99 |
61
|
zred |
|
100 |
|
letr |
|
101 |
24 59 99 100
|
syl3anc |
|
102 |
98 101
|
mpan2d |
|
103 |
96 102
|
sylbid |
|
104 |
92 103
|
syld |
|
105 |
90 104
|
mpan2d |
|
106 |
105
|
adantrd |
|
107 |
106
|
imp |
|
108 |
45 62 64 80 107
|
elfzd |
|
109 |
|
eqid |
|
110 |
|
oveq1 |
|
111 |
110
|
oveq1d |
|
112 |
111
|
rspceeqv |
|
113 |
108 109 112
|
sylancl |
|
114 |
|
ovex |
|
115 |
35
|
elrnmpt |
|
116 |
114 115
|
ax-mp |
|
117 |
113 116
|
sylibr |
|
118 |
|
elun1 |
|
119 |
117 118
|
syl |
|
120 |
|
elun2 |
|
121 |
88 120
|
syl |
|
122 |
121
|
adantr |
|
123 |
119 122
|
ifclda |
|
124 |
123
|
fmpttd |
|
125 |
124
|
frnd |
|
126 |
|
ssfi |
|
127 |
44 125 126
|
syl2anc |
|
128 |
|
eqid |
|
129 |
128
|
mptpreima |
|
130 |
|
unrab |
|
131 |
|
inrab |
|
132 |
131
|
ineq1i |
|
133 |
|
inrab |
|
134 |
132 133
|
eqtri |
|
135 |
|
unrab |
|
136 |
135
|
ineq1i |
|
137 |
|
inrab |
|
138 |
136 137
|
eqtri |
|
139 |
134 138
|
uneq12i |
|
140 |
|
eqcom |
|
141 |
|
fvex |
|
142 |
114 141
|
ifex |
|
143 |
142
|
elsn |
|
144 |
|
ianor |
|
145 |
|
nne |
|
146 |
145
|
orbi2i |
|
147 |
144 146
|
bitr2i |
|
148 |
147
|
anbi1i |
|
149 |
148
|
orbi2i |
|
150 |
|
eqif |
|
151 |
149 150
|
bitr4i |
|
152 |
140 143 151
|
3bitr4i |
|
153 |
152
|
rabbii |
|
154 |
130 139 153
|
3eqtr4ri |
|
155 |
129 154
|
eqtri |
|
156 |
|
eldifi |
|
157 |
32
|
frnd |
|
158 |
157
|
sseld |
|
159 |
156 158
|
syl5 |
|
160 |
159
|
imdistani |
|
161 |
|
rabiun |
|
162 |
|
cnvimarndm |
|
163 |
|
iunid |
|
164 |
163
|
imaeq2i |
|
165 |
|
imaiun |
|
166 |
164 165
|
eqtr3i |
|
167 |
162 166
|
eqtr3i |
|
168 |
28
|
fdmd |
|
169 |
167 168
|
eqtr3id |
|
170 |
169
|
ad2antlr |
|
171 |
|
rabeq |
|
172 |
170 171
|
syl |
|
173 |
161 172
|
eqtr3id |
|
174 |
|
fniniseg |
|
175 |
28 83 174
|
3syl |
|
176 |
175
|
simplbda |
|
177 |
176
|
breq2d |
|
178 |
177
|
rabbidva |
|
179 |
|
inrab2 |
|
180 |
|
imassrn |
|
181 |
|
dfdm4 |
|
182 |
181 168
|
eqtr3id |
|
183 |
180 182
|
sseqtrid |
|
184 |
|
sseqin2 |
|
185 |
183 184
|
sylib |
|
186 |
|
rabeq |
|
187 |
185 186
|
syl |
|
188 |
179 187
|
syl5eq |
|
189 |
178 188
|
eqtr4d |
|
190 |
189
|
ad3antlr |
|
191 |
26
|
adantlr |
|
192 |
46
|
ad2antlr |
|
193 |
192
|
sselda |
|
194 |
193
|
adantr |
|
195 |
69
|
ad3antlr |
|
196 |
191 194 195
|
lemuldivd |
|
197 |
24
|
adantlr |
|
198 |
|
1red |
|
199 |
14
|
ad3antlr |
|
200 |
20
|
ad3antlr |
|
201 |
194 199 200
|
redivcld |
|
202 |
197 198 201
|
lesubaddd |
|
203 |
7
|
adantlr |
|
204 |
|
peano2re |
|
205 |
201 204
|
syl |
|
206 |
|
reflcl |
|
207 |
205 206
|
syl |
|
208 |
|
peano2re |
|
209 |
207 208
|
syl |
|
210 |
203 209 195
|
ltdivmuld |
|
211 |
22
|
adantlr |
|
212 |
|
flflp1 |
|
213 |
211 205 212
|
syl2anc |
|
214 |
199 209
|
remulcld |
|
215 |
214
|
rexrd |
|
216 |
|
elioomnf |
|
217 |
215 216
|
syl |
|
218 |
203
|
biantrurd |
|
219 |
217 218
|
bitr4d |
|
220 |
210 213 219
|
3bitr4d |
|
221 |
196 202 220
|
3bitrd |
|
222 |
221
|
rabbidva |
|
223 |
2
|
feqmptd |
|
224 |
223
|
cnveqd |
|
225 |
224
|
imaeq1d |
|
226 |
|
eqid |
|
227 |
226
|
mptpreima |
|
228 |
225 227
|
eqtrdi |
|
229 |
228
|
ad3antrrr |
|
230 |
222 229
|
eqtr4d |
|
231 |
|
mbfima |
|
232 |
1 5 231
|
syl2anc |
|
233 |
232
|
ad3antrrr |
|
234 |
230 233
|
eqeltrd |
|
235 |
46
|
sseld |
|
236 |
235
|
ad2antlr |
|
237 |
236
|
imdistani |
|
238 |
|
i1fmbf |
|
239 |
238 28
|
jca |
|
240 |
239
|
ad2antlr |
|
241 |
|
mbfimasn |
|
242 |
241
|
3expa |
|
243 |
240 242
|
sylan |
|
244 |
237 243
|
syl |
|
245 |
|
inmbl |
|
246 |
234 244 245
|
syl2anc |
|
247 |
190 246
|
eqeltrd |
|
248 |
247
|
ralrimiva |
|
249 |
|
finiunmbl |
|
250 |
42 248 249
|
syl2anc |
|
251 |
173 250
|
eqeltrrd |
|
252 |
|
unrab |
|
253 |
28
|
feqmptd |
|
254 |
253
|
cnveqd |
|
255 |
254
|
imaeq1d |
|
256 |
|
eqid |
|
257 |
256
|
mptpreima |
|
258 |
255 257
|
eqtrdi |
|
259 |
254
|
imaeq1d |
|
260 |
256
|
mptpreima |
|
261 |
259 260
|
eqtrdi |
|
262 |
258 261
|
uneq12d |
|
263 |
28
|
ffvelrnda |
|
264 |
|
0re |
|
265 |
|
lttri2 |
|
266 |
264 265
|
mpan2 |
|
267 |
|
ibar |
|
268 |
|
andi |
|
269 |
|
0xr |
|
270 |
|
elioomnf |
|
271 |
|
elioopnf |
|
272 |
270 271
|
orbi12d |
|
273 |
269 272
|
ax-mp |
|
274 |
268 273
|
bitr4i |
|
275 |
267 274
|
bitrdi |
|
276 |
266 275
|
bitrd |
|
277 |
263 276
|
syl |
|
278 |
277
|
rabbidva |
|
279 |
252 262 278
|
3eqtr4a |
|
280 |
|
i1fima |
|
281 |
|
i1fima |
|
282 |
|
unmbl |
|
283 |
280 281 282
|
syl2anc |
|
284 |
279 283
|
eqeltrrd |
|
285 |
284
|
ad2antlr |
|
286 |
|
inmbl |
|
287 |
251 285 286
|
syl2anc |
|
288 |
287
|
adantr |
|
289 |
24
|
recnd |
|
290 |
289
|
adantlr |
|
291 |
|
1cnd |
|
292 |
|
simplr |
|
293 |
14
|
ad3antlr |
|
294 |
20
|
ad3antlr |
|
295 |
292 293 294
|
redivcld |
|
296 |
295
|
recnd |
|
297 |
290 291 296
|
subadd2d |
|
298 |
|
eqcom |
|
299 |
|
recn |
|
300 |
299
|
ad2antlr |
|
301 |
26
|
recnd |
|
302 |
301
|
adantlr |
|
303 |
14
|
recnd |
|
304 |
303
|
ad3antlr |
|
305 |
300 302 304 294
|
divmul3d |
|
306 |
298 305
|
syl5bb |
|
307 |
297 306
|
bitr3d |
|
308 |
307
|
rabbidva |
|
309 |
|
imaundi |
|
310 |
224
|
ad4antr |
|
311 |
|
zre |
|
312 |
311
|
adantl |
|
313 |
14
|
ad3antlr |
|
314 |
312 313
|
remulcld |
|
315 |
314
|
rexrd |
|
316 |
|
peano2z |
|
317 |
316
|
zred |
|
318 |
317
|
adantl |
|
319 |
313 318
|
remulcld |
|
320 |
319
|
rexrd |
|
321 |
|
zcn |
|
322 |
321
|
adantl |
|
323 |
303
|
ad3antlr |
|
324 |
322 323
|
mulcomd |
|
325 |
69
|
ad3antlr |
|
326 |
311
|
ltp1d |
|
327 |
326
|
adantl |
|
328 |
312 318 325 327
|
ltmul2dd |
|
329 |
324 328
|
eqbrtrd |
|
330 |
|
snunioo |
|
331 |
315 320 329 330
|
syl3anc |
|
332 |
310 331
|
imaeq12d |
|
333 |
309 332
|
eqtr3id |
|
334 |
226
|
mptpreima |
|
335 |
5
|
ad3antrrr |
|
336 |
335
|
ffvelrnda |
|
337 |
336
|
3biant1d |
|
338 |
337
|
adantr |
|
339 |
311
|
adantl |
|
340 |
336
|
adantr |
|
341 |
69
|
ad4antlr |
|
342 |
339 340 341
|
lemuldivd |
|
343 |
317
|
adantl |
|
344 |
340 343 341
|
ltdivmuld |
|
345 |
344
|
bicomd |
|
346 |
342 345
|
anbi12d |
|
347 |
338 346
|
bitr3d |
|
348 |
|
elico2 |
|
349 |
314 320 348
|
syl2anc |
|
350 |
349
|
adantlr |
|
351 |
|
eqcom |
|
352 |
22
|
adantlr |
|
353 |
|
flbi |
|
354 |
352 353
|
sylan |
|
355 |
351 354
|
syl5bb |
|
356 |
347 350 355
|
3bitr4d |
|
357 |
356
|
an32s |
|
358 |
357
|
rabbidva |
|
359 |
334 358
|
syl5eq |
|
360 |
333 359
|
eqtrd |
|
361 |
1
|
ad4antr |
|
362 |
5
|
ad4antr |
|
363 |
|
mbfimasn |
|
364 |
361 362 314 363
|
syl3anc |
|
365 |
|
mbfima |
|
366 |
1 5 365
|
syl2anc |
|
367 |
366
|
ad4antr |
|
368 |
|
unmbl |
|
369 |
364 367 368
|
syl2anc |
|
370 |
360 369
|
eqeltrrd |
|
371 |
|
simpr |
|
372 |
352
|
flcld |
|
373 |
372
|
adantr |
|
374 |
371 373
|
eqeltrd |
|
375 |
374
|
stoic1a |
|
376 |
375
|
an32s |
|
377 |
376
|
ralrimiva |
|
378 |
|
rabeq0 |
|
379 |
377 378
|
sylibr |
|
380 |
|
0mbl |
|
381 |
379 380
|
eqeltrdi |
|
382 |
370 381
|
pm2.61dan |
|
383 |
308 382
|
eqeltrrd |
|
384 |
|
inmbl |
|
385 |
288 383 384
|
syl2anc |
|
386 |
|
rabiun |
|
387 |
|
rabeq |
|
388 |
169 387
|
syl |
|
389 |
386 388
|
eqtr3id |
|
390 |
389
|
ad2antlr |
|
391 |
177
|
notbid |
|
392 |
391
|
rabbidva |
|
393 |
|
inrab2 |
|
394 |
|
rabeq |
|
395 |
185 394
|
syl |
|
396 |
393 395
|
syl5eq |
|
397 |
392 396
|
eqtr4d |
|
398 |
397
|
ad3antlr |
|
399 |
|
imaundi |
|
400 |
14 20
|
jca |
|
401 |
|
redivcl |
|
402 |
401
|
3expb |
|
403 |
400 402
|
sylan2 |
|
404 |
403
|
ancoms |
|
405 |
404
|
adantll |
|
406 |
405 204
|
syl |
|
407 |
|
peano2re |
|
408 |
|
reflcl |
|
409 |
406 407 408
|
3syl |
|
410 |
14
|
ad2antlr |
|
411 |
409 410
|
remulcld |
|
412 |
411
|
rexrd |
|
413 |
|
pnfxr |
|
414 |
413
|
a1i |
|
415 |
|
ltpnf |
|
416 |
411 415
|
syl |
|
417 |
|
snunioo |
|
418 |
412 414 416 417
|
syl3anc |
|
419 |
418
|
imaeq2d |
|
420 |
399 419
|
eqtr3id |
|
421 |
224
|
imaeq1d |
|
422 |
226
|
mptpreima |
|
423 |
421 422
|
eqtrdi |
|
424 |
423
|
ad3antrrr |
|
425 |
406 407
|
syl |
|
426 |
425
|
adantr |
|
427 |
|
flflp1 |
|
428 |
426 352 427
|
syl2anc |
|
429 |
411
|
adantr |
|
430 |
|
elicopnf |
|
431 |
429 430
|
syl |
|
432 |
336
|
biantrurd |
|
433 |
409
|
adantr |
|
434 |
69
|
ad3antlr |
|
435 |
433 336 434
|
lemuldivd |
|
436 |
431 432 435
|
3bitr2d |
|
437 |
406
|
adantr |
|
438 |
352 23
|
syl |
|
439 |
|
1red |
|
440 |
437 438 439
|
ltadd1d |
|
441 |
428 436 440
|
3bitr4d |
|
442 |
295 439 438
|
ltaddsubd |
|
443 |
441 442
|
bitrd |
|
444 |
438 25
|
syl |
|
445 |
292 444 434
|
ltdivmul2d |
|
446 |
444 293
|
remulcld |
|
447 |
292 446
|
ltnled |
|
448 |
443 445 447
|
3bitrd |
|
449 |
448
|
rabbidva |
|
450 |
420 424 449
|
3eqtrd |
|
451 |
1
|
ad3antrrr |
|
452 |
|
mbfimasn |
|
453 |
451 335 411 452
|
syl3anc |
|
454 |
|
mbfima |
|
455 |
1 5 454
|
syl2anc |
|
456 |
455
|
ad3antrrr |
|
457 |
|
unmbl |
|
458 |
453 456 457
|
syl2anc |
|
459 |
450 458
|
eqeltrrd |
|
460 |
237 459
|
syl |
|
461 |
|
inmbl |
|
462 |
460 244 461
|
syl2anc |
|
463 |
398 462
|
eqeltrd |
|
464 |
463
|
ralrimiva |
|
465 |
|
finiunmbl |
|
466 |
42 464 465
|
syl2anc |
|
467 |
390 466
|
eqeltrrd |
|
468 |
254
|
imaeq1d |
|
469 |
256
|
mptpreima |
|
470 |
141
|
elsn |
|
471 |
470
|
rabbii |
|
472 |
469 471
|
eqtri |
|
473 |
468 472
|
eqtrdi |
|
474 |
|
i1fima |
|
475 |
473 474
|
eqeltrrd |
|
476 |
475
|
ad2antlr |
|
477 |
|
unmbl |
|
478 |
467 476 477
|
syl2anc |
|
479 |
478
|
adantr |
|
480 |
254
|
imaeq1d |
|
481 |
256
|
mptpreima |
|
482 |
141
|
elsn |
|
483 |
|
eqcom |
|
484 |
482 483
|
bitri |
|
485 |
484
|
rabbii |
|
486 |
481 485
|
eqtri |
|
487 |
480 486
|
eqtrdi |
|
488 |
487
|
ad3antlr |
|
489 |
488 243
|
eqeltrrd |
|
490 |
|
inmbl |
|
491 |
479 489 490
|
syl2anc |
|
492 |
|
unmbl |
|
493 |
385 491 492
|
syl2anc |
|
494 |
160 493
|
syl |
|
495 |
155 494
|
eqeltrid |
|
496 |
|
mblvol |
|
497 |
495 496
|
syl |
|
498 |
|
eldifsn |
|
499 |
158
|
anim1d |
|
500 |
498 499
|
syl5bi |
|
501 |
500
|
imdistani |
|
502 |
129
|
a1i |
|
503 |
468 469
|
eqtrdi |
|
504 |
502 503
|
ineq12d |
|
505 |
|
inrab |
|
506 |
504 505
|
eqtrdi |
|
507 |
506
|
ad3antlr |
|
508 |
145
|
biimpri |
|
509 |
508
|
intnand |
|
510 |
509
|
iffalsed |
|
511 |
|
eqtr |
|
512 |
510 511
|
mpancom |
|
513 |
512
|
adantl |
|
514 |
|
simpll |
|
515 |
514
|
necomd |
|
516 |
513 515
|
eqnetrd |
|
517 |
516
|
ex |
|
518 |
|
orcom |
|
519 |
|
ianor |
|
520 |
|
imor |
|
521 |
518 519 520
|
3bitr4i |
|
522 |
143
|
necon3bbii |
|
523 |
470 522
|
imbi12i |
|
524 |
521 523
|
bitri |
|
525 |
517 524
|
sylibr |
|
526 |
525
|
ralrimiva |
|
527 |
|
rabeq0 |
|
528 |
526 527
|
sylibr |
|
529 |
528
|
ad2antll |
|
530 |
507 529
|
eqtrd |
|
531 |
|
imassrn |
|
532 |
|
dfdm4 |
|
533 |
142 128
|
dmmpti |
|
534 |
532 533
|
eqtr3i |
|
535 |
531 534
|
sseqtri |
|
536 |
|
reldisj |
|
537 |
535 536
|
ax-mp |
|
538 |
530 537
|
sylib |
|
539 |
|
ffun |
|
540 |
|
difpreima |
|
541 |
539 540
|
syl |
|
542 |
|
fdm |
|
543 |
162 542
|
syl5eq |
|
544 |
543
|
difeq1d |
|
545 |
541 544
|
eqtrd |
|
546 |
28 545
|
syl |
|
547 |
546
|
ad3antlr |
|
548 |
538 547
|
sseqtrrd |
|
549 |
|
imassrn |
|
550 |
549 182
|
sseqtrid |
|
551 |
550
|
ad3antlr |
|
552 |
|
i1fima |
|
553 |
|
mblvol |
|
554 |
552 553
|
syl |
|
555 |
|
neldifsn |
|
556 |
|
i1fima2 |
|
557 |
555 556
|
mpan2 |
|
558 |
554 557
|
eqeltrrd |
|
559 |
558
|
ad3antlr |
|
560 |
|
ovolsscl |
|
561 |
548 551 559 560
|
syl3anc |
|
562 |
501 561
|
syl |
|
563 |
497 562
|
eqeltrd |
|
564 |
32 127 495 563
|
i1fd |
|