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 |
|
3nn |
|
46 |
|
nnrp |
|
47 |
45 46
|
ax-mp |
|
48 |
|
rpdivcl |
|
49 |
47 48
|
mpan2 |
|
50 |
49
|
ad2antlr |
|
51 |
2
|
ad2antrr |
|
52 |
51
|
ffvelrnda |
|
53 |
|
elrege0 |
|
54 |
52 53
|
sylib |
|
55 |
54
|
simprd |
|
56 |
7 50 55
|
divge0d |
|
57 |
|
flge0nn0 |
|
58 |
22 56 57
|
syl2anc |
|
59 |
58
|
nn0ge0d |
|
60 |
59
|
adantr |
|
61 |
28
|
frnd |
|
62 |
|
i1f0rn |
|
63 |
|
elex2 |
|
64 |
62 63
|
syl |
|
65 |
|
n0 |
|
66 |
64 65
|
sylibr |
|
67 |
|
fimaxre2 |
|
68 |
61 41 67
|
syl2anc |
|
69 |
61 66 68
|
3jca |
|
70 |
69
|
ad3antlr |
|
71 |
|
ffn |
|
72 |
28 71
|
syl |
|
73 |
|
dffn3 |
|
74 |
72 73
|
sylib |
|
75 |
74
|
ad2antlr |
|
76 |
75
|
ffvelrnda |
|
77 |
|
suprub |
|
78 |
70 76 77
|
syl2anc |
|
79 |
|
suprcl |
|
80 |
61 66 68 79
|
syl3anc |
|
81 |
80
|
ad3antlr |
|
82 |
|
letr |
|
83 |
27 30 81 82
|
syl3anc |
|
84 |
26 81 50
|
lemuldivd |
|
85 |
|
1red |
|
86 |
81 15 21
|
redivcld |
|
87 |
24 85 86
|
lesubaddd |
|
88 |
84 87
|
bitrd |
|
89 |
|
peano2re |
|
90 |
86 89
|
syl |
|
91 |
|
ceige |
|
92 |
90 91
|
syl |
|
93 |
|
ceicl |
|
94 |
90 93
|
syl |
|
95 |
94
|
zred |
|
96 |
|
letr |
|
97 |
24 90 95 96
|
syl3anc |
|
98 |
92 97
|
mpan2d |
|
99 |
88 98
|
sylbid |
|
100 |
83 99
|
syld |
|
101 |
78 100
|
mpan2d |
|
102 |
101
|
adantrd |
|
103 |
102
|
imp |
|
104 |
22
|
flcld |
|
105 |
104
|
adantr |
|
106 |
|
0zd |
|
107 |
94
|
adantr |
|
108 |
|
elfz |
|
109 |
105 106 107 108
|
syl3anc |
|
110 |
60 103 109
|
mpbir2and |
|
111 |
|
eqid |
|
112 |
|
oveq1 |
|
113 |
112
|
oveq1d |
|
114 |
113
|
rspceeqv |
|
115 |
110 111 114
|
sylancl |
|
116 |
|
ovex |
|
117 |
35
|
elrnmpt |
|
118 |
116 117
|
ax-mp |
|
119 |
115 118
|
sylibr |
|
120 |
|
elun1 |
|
121 |
119 120
|
syl |
|
122 |
|
elun2 |
|
123 |
76 122
|
syl |
|
124 |
123
|
adantr |
|
125 |
121 124
|
ifclda |
|
126 |
125
|
fmpttd |
|
127 |
126
|
frnd |
|
128 |
|
ssfi |
|
129 |
44 127 128
|
syl2anc |
|
130 |
|
eqid |
|
131 |
130
|
mptpreima |
|
132 |
|
unrab |
|
133 |
|
inrab |
|
134 |
133
|
ineq1i |
|
135 |
|
inrab |
|
136 |
134 135
|
eqtri |
|
137 |
|
unrab |
|
138 |
137
|
ineq1i |
|
139 |
|
inrab |
|
140 |
138 139
|
eqtri |
|
141 |
136 140
|
uneq12i |
|
142 |
|
eqcom |
|
143 |
|
fvex |
|
144 |
116 143
|
ifex |
|
145 |
144
|
elsn |
|
146 |
|
ianor |
|
147 |
|
nne |
|
148 |
147
|
orbi2i |
|
149 |
146 148
|
bitr2i |
|
150 |
149
|
anbi1i |
|
151 |
150
|
orbi2i |
|
152 |
|
eqif |
|
153 |
151 152
|
bitr4i |
|
154 |
142 145 153
|
3bitr4i |
|
155 |
154
|
rabbii |
|
156 |
132 141 155
|
3eqtr4ri |
|
157 |
131 156
|
eqtri |
|
158 |
|
eldifi |
|
159 |
32
|
frnd |
|
160 |
159
|
sseld |
|
161 |
158 160
|
syl5 |
|
162 |
161
|
imdistani |
|
163 |
|
rabiun |
|
164 |
|
cnvimarndm |
|
165 |
|
iunid |
|
166 |
165
|
imaeq2i |
|
167 |
|
imaiun |
|
168 |
166 167
|
eqtr3i |
|
169 |
164 168
|
eqtr3i |
|
170 |
28
|
fdmd |
|
171 |
169 170
|
syl5eqr |
|
172 |
171
|
ad2antlr |
|
173 |
|
rabeq |
|
174 |
172 173
|
syl |
|
175 |
163 174
|
syl5eqr |
|
176 |
|
fniniseg |
|
177 |
28 71 176
|
3syl |
|
178 |
177
|
simplbda |
|
179 |
178
|
breq2d |
|
180 |
179
|
rabbidva |
|
181 |
|
inrab2 |
|
182 |
|
imassrn |
|
183 |
|
dfdm4 |
|
184 |
183 170
|
syl5eqr |
|
185 |
182 184
|
sseqtrid |
|
186 |
|
sseqin2 |
|
187 |
185 186
|
sylib |
|
188 |
|
rabeq |
|
189 |
187 188
|
syl |
|
190 |
181 189
|
syl5eq |
|
191 |
180 190
|
eqtr4d |
|
192 |
191
|
ad3antlr |
|
193 |
26
|
adantlr |
|
194 |
61
|
ad2antlr |
|
195 |
194
|
sselda |
|
196 |
195
|
adantr |
|
197 |
49
|
ad3antlr |
|
198 |
193 196 197
|
lemuldivd |
|
199 |
24
|
adantlr |
|
200 |
|
1red |
|
201 |
14
|
ad3antlr |
|
202 |
20
|
ad3antlr |
|
203 |
196 201 202
|
redivcld |
|
204 |
199 200 203
|
lesubaddd |
|
205 |
7
|
adantlr |
|
206 |
|
peano2re |
|
207 |
203 206
|
syl |
|
208 |
|
reflcl |
|
209 |
207 208
|
syl |
|
210 |
|
peano2re |
|
211 |
209 210
|
syl |
|
212 |
205 211 197
|
ltdivmuld |
|
213 |
22
|
adantlr |
|
214 |
|
flflp1 |
|
215 |
213 207 214
|
syl2anc |
|
216 |
201 211
|
remulcld |
|
217 |
216
|
rexrd |
|
218 |
|
elioomnf |
|
219 |
217 218
|
syl |
|
220 |
205
|
biantrurd |
|
221 |
219 220
|
bitr4d |
|
222 |
212 215 221
|
3bitr4d |
|
223 |
198 204 222
|
3bitrd |
|
224 |
223
|
rabbidva |
|
225 |
2
|
feqmptd |
|
226 |
225
|
cnveqd |
|
227 |
226
|
imaeq1d |
|
228 |
|
eqid |
|
229 |
228
|
mptpreima |
|
230 |
227 229
|
eqtrdi |
|
231 |
230
|
ad3antrrr |
|
232 |
224 231
|
eqtr4d |
|
233 |
|
mbfima |
|
234 |
1 5 233
|
syl2anc |
|
235 |
234
|
ad3antrrr |
|
236 |
232 235
|
eqeltrd |
|
237 |
61
|
sseld |
|
238 |
237
|
ad2antlr |
|
239 |
238
|
imdistani |
|
240 |
|
i1fmbf |
|
241 |
240 28
|
jca |
|
242 |
241
|
ad2antlr |
|
243 |
|
mbfimasn |
|
244 |
243
|
3expa |
|
245 |
242 244
|
sylan |
|
246 |
239 245
|
syl |
|
247 |
|
inmbl |
|
248 |
236 246 247
|
syl2anc |
|
249 |
192 248
|
eqeltrd |
|
250 |
249
|
ralrimiva |
|
251 |
|
finiunmbl |
|
252 |
42 250 251
|
syl2anc |
|
253 |
175 252
|
eqeltrrd |
|
254 |
|
unrab |
|
255 |
28
|
feqmptd |
|
256 |
255
|
cnveqd |
|
257 |
256
|
imaeq1d |
|
258 |
|
eqid |
|
259 |
258
|
mptpreima |
|
260 |
257 259
|
eqtrdi |
|
261 |
256
|
imaeq1d |
|
262 |
258
|
mptpreima |
|
263 |
261 262
|
eqtrdi |
|
264 |
260 263
|
uneq12d |
|
265 |
28
|
ffvelrnda |
|
266 |
|
0re |
|
267 |
|
lttri2 |
|
268 |
266 267
|
mpan2 |
|
269 |
|
ibar |
|
270 |
|
andi |
|
271 |
|
0xr |
|
272 |
|
elioomnf |
|
273 |
|
elioopnf |
|
274 |
272 273
|
orbi12d |
|
275 |
271 274
|
ax-mp |
|
276 |
270 275
|
bitr4i |
|
277 |
269 276
|
syl6bb |
|
278 |
268 277
|
bitrd |
|
279 |
265 278
|
syl |
|
280 |
279
|
rabbidva |
|
281 |
254 264 280
|
3eqtr4a |
|
282 |
|
i1fima |
|
283 |
|
i1fima |
|
284 |
|
unmbl |
|
285 |
282 283 284
|
syl2anc |
|
286 |
281 285
|
eqeltrrd |
|
287 |
286
|
ad2antlr |
|
288 |
|
inmbl |
|
289 |
253 287 288
|
syl2anc |
|
290 |
289
|
adantr |
|
291 |
24
|
recnd |
|
292 |
291
|
adantlr |
|
293 |
|
1cnd |
|
294 |
|
simplr |
|
295 |
14
|
ad3antlr |
|
296 |
20
|
ad3antlr |
|
297 |
294 295 296
|
redivcld |
|
298 |
297
|
recnd |
|
299 |
292 293 298
|
subadd2d |
|
300 |
|
eqcom |
|
301 |
|
recn |
|
302 |
301
|
ad2antlr |
|
303 |
26
|
recnd |
|
304 |
303
|
adantlr |
|
305 |
14
|
recnd |
|
306 |
305
|
ad3antlr |
|
307 |
302 304 306 296
|
divmul3d |
|
308 |
300 307
|
syl5bb |
|
309 |
299 308
|
bitr3d |
|
310 |
309
|
rabbidva |
|
311 |
|
imaundi |
|
312 |
226
|
ad4antr |
|
313 |
|
zre |
|
314 |
313
|
adantl |
|
315 |
14
|
ad3antlr |
|
316 |
314 315
|
remulcld |
|
317 |
316
|
rexrd |
|
318 |
|
peano2z |
|
319 |
318
|
zred |
|
320 |
319
|
adantl |
|
321 |
315 320
|
remulcld |
|
322 |
321
|
rexrd |
|
323 |
|
zcn |
|
324 |
323
|
adantl |
|
325 |
305
|
ad3antlr |
|
326 |
324 325
|
mulcomd |
|
327 |
49
|
ad3antlr |
|
328 |
313
|
ltp1d |
|
329 |
328
|
adantl |
|
330 |
314 320 327 329
|
ltmul2dd |
|
331 |
326 330
|
eqbrtrd |
|
332 |
|
snunioo |
|
333 |
317 322 331 332
|
syl3anc |
|
334 |
312 333
|
imaeq12d |
|
335 |
311 334
|
syl5eqr |
|
336 |
228
|
mptpreima |
|
337 |
5
|
ad3antrrr |
|
338 |
337
|
ffvelrnda |
|
339 |
338
|
3biant1d |
|
340 |
339
|
adantr |
|
341 |
313
|
adantl |
|
342 |
338
|
adantr |
|
343 |
49
|
ad4antlr |
|
344 |
341 342 343
|
lemuldivd |
|
345 |
319
|
adantl |
|
346 |
342 345 343
|
ltdivmuld |
|
347 |
346
|
bicomd |
|
348 |
344 347
|
anbi12d |
|
349 |
340 348
|
bitr3d |
|
350 |
|
elico2 |
|
351 |
316 322 350
|
syl2anc |
|
352 |
351
|
adantlr |
|
353 |
|
eqcom |
|
354 |
22
|
adantlr |
|
355 |
|
flbi |
|
356 |
354 355
|
sylan |
|
357 |
353 356
|
syl5bb |
|
358 |
349 352 357
|
3bitr4d |
|
359 |
358
|
an32s |
|
360 |
359
|
rabbidva |
|
361 |
336 360
|
syl5eq |
|
362 |
335 361
|
eqtrd |
|
363 |
1
|
ad4antr |
|
364 |
5
|
ad4antr |
|
365 |
|
mbfimasn |
|
366 |
363 364 316 365
|
syl3anc |
|
367 |
|
mbfima |
|
368 |
1 5 367
|
syl2anc |
|
369 |
368
|
ad4antr |
|
370 |
|
unmbl |
|
371 |
366 369 370
|
syl2anc |
|
372 |
362 371
|
eqeltrrd |
|
373 |
|
simpr |
|
374 |
354
|
flcld |
|
375 |
374
|
adantr |
|
376 |
373 375
|
eqeltrd |
|
377 |
376
|
stoic1a |
|
378 |
377
|
an32s |
|
379 |
378
|
ralrimiva |
|
380 |
|
rabeq0 |
|
381 |
379 380
|
sylibr |
|
382 |
|
0mbl |
|
383 |
381 382
|
eqeltrdi |
|
384 |
372 383
|
pm2.61dan |
|
385 |
310 384
|
eqeltrrd |
|
386 |
|
inmbl |
|
387 |
290 385 386
|
syl2anc |
|
388 |
|
rabiun |
|
389 |
|
rabeq |
|
390 |
171 389
|
syl |
|
391 |
388 390
|
syl5eqr |
|
392 |
391
|
ad2antlr |
|
393 |
179
|
notbid |
|
394 |
393
|
rabbidva |
|
395 |
|
inrab2 |
|
396 |
|
rabeq |
|
397 |
187 396
|
syl |
|
398 |
395 397
|
syl5eq |
|
399 |
394 398
|
eqtr4d |
|
400 |
399
|
ad3antlr |
|
401 |
|
imaundi |
|
402 |
14 20
|
jca |
|
403 |
|
redivcl |
|
404 |
403
|
3expb |
|
405 |
402 404
|
sylan2 |
|
406 |
405
|
ancoms |
|
407 |
406
|
adantll |
|
408 |
407 206
|
syl |
|
409 |
|
peano2re |
|
410 |
|
reflcl |
|
411 |
408 409 410
|
3syl |
|
412 |
14
|
ad2antlr |
|
413 |
411 412
|
remulcld |
|
414 |
413
|
rexrd |
|
415 |
|
pnfxr |
|
416 |
415
|
a1i |
|
417 |
|
ltpnf |
|
418 |
413 417
|
syl |
|
419 |
|
snunioo |
|
420 |
414 416 418 419
|
syl3anc |
|
421 |
420
|
imaeq2d |
|
422 |
401 421
|
syl5eqr |
|
423 |
226
|
imaeq1d |
|
424 |
228
|
mptpreima |
|
425 |
423 424
|
eqtrdi |
|
426 |
425
|
ad3antrrr |
|
427 |
408 409
|
syl |
|
428 |
427
|
adantr |
|
429 |
|
flflp1 |
|
430 |
428 354 429
|
syl2anc |
|
431 |
413
|
adantr |
|
432 |
|
elicopnf |
|
433 |
431 432
|
syl |
|
434 |
338
|
biantrurd |
|
435 |
411
|
adantr |
|
436 |
49
|
ad3antlr |
|
437 |
435 338 436
|
lemuldivd |
|
438 |
433 434 437
|
3bitr2d |
|
439 |
408
|
adantr |
|
440 |
354 23
|
syl |
|
441 |
|
1red |
|
442 |
439 440 441
|
ltadd1d |
|
443 |
430 438 442
|
3bitr4d |
|
444 |
297 441 440
|
ltaddsubd |
|
445 |
443 444
|
bitrd |
|
446 |
440 25
|
syl |
|
447 |
294 446 436
|
ltdivmul2d |
|
448 |
446 295
|
remulcld |
|
449 |
294 448
|
ltnled |
|
450 |
445 447 449
|
3bitrd |
|
451 |
450
|
rabbidva |
|
452 |
422 426 451
|
3eqtrd |
|
453 |
1
|
ad3antrrr |
|
454 |
|
mbfimasn |
|
455 |
453 337 413 454
|
syl3anc |
|
456 |
|
mbfima |
|
457 |
1 5 456
|
syl2anc |
|
458 |
457
|
ad3antrrr |
|
459 |
|
unmbl |
|
460 |
455 458 459
|
syl2anc |
|
461 |
452 460
|
eqeltrrd |
|
462 |
239 461
|
syl |
|
463 |
|
inmbl |
|
464 |
462 246 463
|
syl2anc |
|
465 |
400 464
|
eqeltrd |
|
466 |
465
|
ralrimiva |
|
467 |
|
finiunmbl |
|
468 |
42 466 467
|
syl2anc |
|
469 |
392 468
|
eqeltrrd |
|
470 |
256
|
imaeq1d |
|
471 |
258
|
mptpreima |
|
472 |
143
|
elsn |
|
473 |
472
|
rabbii |
|
474 |
471 473
|
eqtri |
|
475 |
470 474
|
eqtrdi |
|
476 |
|
i1fima |
|
477 |
475 476
|
eqeltrrd |
|
478 |
477
|
ad2antlr |
|
479 |
|
unmbl |
|
480 |
469 478 479
|
syl2anc |
|
481 |
480
|
adantr |
|
482 |
256
|
imaeq1d |
|
483 |
258
|
mptpreima |
|
484 |
143
|
elsn |
|
485 |
|
eqcom |
|
486 |
484 485
|
bitri |
|
487 |
486
|
rabbii |
|
488 |
483 487
|
eqtri |
|
489 |
482 488
|
eqtrdi |
|
490 |
489
|
ad3antlr |
|
491 |
490 245
|
eqeltrrd |
|
492 |
|
inmbl |
|
493 |
481 491 492
|
syl2anc |
|
494 |
|
unmbl |
|
495 |
387 493 494
|
syl2anc |
|
496 |
162 495
|
syl |
|
497 |
157 496
|
eqeltrid |
|
498 |
|
mblvol |
|
499 |
497 498
|
syl |
|
500 |
|
eldifsn |
|
501 |
160
|
anim1d |
|
502 |
500 501
|
syl5bi |
|
503 |
502
|
imdistani |
|
504 |
131
|
a1i |
|
505 |
470 471
|
eqtrdi |
|
506 |
504 505
|
ineq12d |
|
507 |
|
inrab |
|
508 |
506 507
|
eqtrdi |
|
509 |
508
|
ad3antlr |
|
510 |
147
|
biimpri |
|
511 |
510
|
intnand |
|
512 |
511
|
iffalsed |
|
513 |
|
eqtr |
|
514 |
512 513
|
mpancom |
|
515 |
514
|
adantl |
|
516 |
|
simpll |
|
517 |
516
|
necomd |
|
518 |
515 517
|
eqnetrd |
|
519 |
518
|
ex |
|
520 |
|
orcom |
|
521 |
|
ianor |
|
522 |
|
imor |
|
523 |
520 521 522
|
3bitr4i |
|
524 |
145
|
necon3bbii |
|
525 |
472 524
|
imbi12i |
|
526 |
523 525
|
bitri |
|
527 |
519 526
|
sylibr |
|
528 |
527
|
ralrimiva |
|
529 |
|
rabeq0 |
|
530 |
528 529
|
sylibr |
|
531 |
530
|
ad2antll |
|
532 |
509 531
|
eqtrd |
|
533 |
|
imassrn |
|
534 |
|
dfdm4 |
|
535 |
144 130
|
dmmpti |
|
536 |
534 535
|
eqtr3i |
|
537 |
533 536
|
sseqtri |
|
538 |
|
reldisj |
|
539 |
537 538
|
ax-mp |
|
540 |
532 539
|
sylib |
|
541 |
|
ffun |
|
542 |
|
difpreima |
|
543 |
541 542
|
syl |
|
544 |
|
fdm |
|
545 |
164 544
|
syl5eq |
|
546 |
545
|
difeq1d |
|
547 |
543 546
|
eqtrd |
|
548 |
28 547
|
syl |
|
549 |
548
|
ad3antlr |
|
550 |
540 549
|
sseqtrrd |
|
551 |
|
imassrn |
|
552 |
551 184
|
sseqtrid |
|
553 |
552
|
ad3antlr |
|
554 |
|
i1fima |
|
555 |
|
mblvol |
|
556 |
554 555
|
syl |
|
557 |
|
neldifsn |
|
558 |
|
i1fima2 |
|
559 |
557 558
|
mpan2 |
|
560 |
556 559
|
eqeltrrd |
|
561 |
560
|
ad3antlr |
|
562 |
|
ovolsscl |
|
563 |
550 553 561 562
|
syl3anc |
|
564 |
503 563
|
syl |
|
565 |
499 564
|
eqeltrd |
|
566 |
32 129 497 565
|
i1fd |
|