Step |
Hyp |
Ref |
Expression |
1 |
|
heicant.c |
|
2 |
|
heicant.d |
|
3 |
|
heicant.j |
|
4 |
|
heicant.x |
|
5 |
|
heicant.y |
|
6 |
|
breq2 |
|
7 |
6
|
imbi2d |
|
8 |
7
|
2ralbidv |
|
9 |
8
|
rexbidv |
|
10 |
9
|
cbvralvw |
|
11 |
|
r19.12 |
|
12 |
11
|
ralimi |
|
13 |
10 12
|
sylbi |
|
14 |
|
rphalfcl |
|
15 |
|
breq2 |
|
16 |
15
|
imbi2d |
|
17 |
16
|
ralbidv |
|
18 |
17
|
rexbidv |
|
19 |
18
|
ralbidv |
|
20 |
19
|
rspcva |
|
21 |
3
|
ad3antrrr |
|
22 |
1
|
ad2antrr |
|
23 |
22
|
anim1i |
|
24 |
|
rphalfcl |
|
25 |
24
|
rpxrd |
|
26 |
|
eqid |
|
27 |
26
|
blopn |
|
28 |
27
|
3expa |
|
29 |
23 25 28
|
syl2an |
|
30 |
29
|
adantr |
|
31 |
24
|
rpgt0d |
|
32 |
25 31
|
jca |
|
33 |
|
xblcntr |
|
34 |
33
|
3expa |
|
35 |
23 32 34
|
syl2an |
|
36 |
35
|
adantr |
|
37 |
|
opelxpi |
|
38 |
24 37
|
sylan2 |
|
39 |
38
|
ad4ant23 |
|
40 |
|
rpcn |
|
41 |
40
|
2halvesd |
|
42 |
41
|
breq2d |
|
43 |
42
|
imbi1d |
|
44 |
43
|
ralbidv |
|
45 |
|
oveq2 |
|
46 |
45
|
breq1d |
|
47 |
|
fveq2 |
|
48 |
47
|
oveq2d |
|
49 |
48
|
breq1d |
|
50 |
46 49
|
imbi12d |
|
51 |
50
|
cbvralvw |
|
52 |
44 51
|
bitrdi |
|
53 |
52
|
biimpar |
|
54 |
53
|
adantll |
|
55 |
|
vex |
|
56 |
|
ovex |
|
57 |
55 56
|
op1std |
|
58 |
55 56
|
op2ndd |
|
59 |
57 58
|
oveq12d |
|
60 |
59
|
eqcomd |
|
61 |
60
|
biantrurd |
|
62 |
57
|
oveq1d |
|
63 |
58 58
|
oveq12d |
|
64 |
62 63
|
breq12d |
|
65 |
57
|
fveq2d |
|
66 |
65
|
oveq1d |
|
67 |
66
|
breq1d |
|
68 |
64 67
|
imbi12d |
|
69 |
68
|
ralbidv |
|
70 |
61 69
|
bitr3d |
|
71 |
70
|
rspcev |
|
72 |
39 54 71
|
syl2anc |
|
73 |
|
eleq2 |
|
74 |
|
eqeq1 |
|
75 |
74
|
anbi1d |
|
76 |
75
|
rexbidv |
|
77 |
73 76
|
anbi12d |
|
78 |
77
|
rspcev |
|
79 |
30 36 72 78
|
syl12anc |
|
80 |
79
|
rexlimdva2 |
|
81 |
80
|
ralimdva |
|
82 |
81
|
imp |
|
83 |
26
|
mopnuni |
|
84 |
1 83
|
syl |
|
85 |
84
|
raleqdv |
|
86 |
85
|
ad3antrrr |
|
87 |
82 86
|
mpbid |
|
88 |
|
eqid |
|
89 |
|
fveq2 |
|
90 |
|
fveq2 |
|
91 |
89 90
|
oveq12d |
|
92 |
91
|
eqeq2d |
|
93 |
89
|
oveq1d |
|
94 |
90 90
|
oveq12d |
|
95 |
93 94
|
breq12d |
|
96 |
89
|
fveq2d |
|
97 |
96
|
oveq1d |
|
98 |
97
|
breq1d |
|
99 |
95 98
|
imbi12d |
|
100 |
99
|
ralbidv |
|
101 |
92 100
|
anbi12d |
|
102 |
88 101
|
cmpcovf |
|
103 |
21 87 102
|
syl2anc |
|
104 |
103
|
ex |
|
105 |
|
elinel2 |
|
106 |
|
simpll |
|
107 |
106
|
anim1i |
|
108 |
|
frn |
|
109 |
|
rnss |
|
110 |
108 109
|
syl |
|
111 |
|
rnxpss |
|
112 |
110 111
|
sstrdi |
|
113 |
112
|
adantl |
|
114 |
|
simplr |
|
115 |
|
ffun |
|
116 |
|
vex |
|
117 |
116
|
fundmen |
|
118 |
117
|
ensymd |
|
119 |
115 118
|
syl |
|
120 |
|
fdm |
|
121 |
119 120
|
breqtrd |
|
122 |
|
enfii |
|
123 |
121 122
|
sylan2 |
|
124 |
|
rnfi |
|
125 |
|
rnfi |
|
126 |
123 124 125
|
3syl |
|
127 |
114 126
|
sylan |
|
128 |
120
|
adantl |
|
129 |
|
eqtr |
|
130 |
84 129
|
sylan |
|
131 |
4
|
adantr |
|
132 |
130 131
|
eqnetrrd |
|
133 |
|
unieq |
|
134 |
|
uni0 |
|
135 |
133 134
|
eqtrdi |
|
136 |
135
|
necon3i |
|
137 |
132 136
|
syl |
|
138 |
137
|
adantr |
|
139 |
128 138
|
eqnetrd |
|
140 |
|
dm0rn0 |
|
141 |
140
|
necon3bii |
|
142 |
139 141
|
sylib |
|
143 |
|
relxp |
|
144 |
|
relss |
|
145 |
108 143 144
|
mpisyl |
|
146 |
|
relrn0 |
|
147 |
146
|
necon3bid |
|
148 |
145 147
|
syl |
|
149 |
148
|
adantl |
|
150 |
142 149
|
mpbid |
|
151 |
150
|
adantllr |
|
152 |
|
rpssre |
|
153 |
113 152
|
sstrdi |
|
154 |
|
ltso |
|
155 |
|
fiinfcl |
|
156 |
154 155
|
mpan |
|
157 |
127 151 153 156
|
syl3anc |
|
158 |
113 157
|
sseldd |
|
159 |
107 158
|
sylanl1 |
|
160 |
159
|
adantr |
|
161 |
84
|
ad3antrrr |
|
162 |
161
|
anim1i |
|
163 |
162
|
ad2antrr |
|
164 |
|
simpl |
|
165 |
129
|
eleq2d |
|
166 |
|
eluni2 |
|
167 |
165 166
|
bitrdi |
|
168 |
167
|
biimpa |
|
169 |
163 164 168
|
syl2an |
|
170 |
|
nfv |
|
171 |
|
nfra1 |
|
172 |
170 171
|
nfan |
|
173 |
|
nfv |
|
174 |
172 173
|
nfan |
|
175 |
|
nfv |
|
176 |
|
rspa |
|
177 |
|
oveq2 |
|
178 |
177
|
breq1d |
|
179 |
|
fveq2 |
|
180 |
179
|
oveq2d |
|
181 |
180
|
breq1d |
|
182 |
178 181
|
imbi12d |
|
183 |
182
|
rspcva |
|
184 |
|
oveq2 |
|
185 |
184
|
breq1d |
|
186 |
47
|
oveq2d |
|
187 |
186
|
breq1d |
|
188 |
185 187
|
imbi12d |
|
189 |
188
|
rspcva |
|
190 |
183 189
|
anim12i |
|
191 |
190
|
anandirs |
|
192 |
|
anim12 |
|
193 |
191 192
|
syl |
|
194 |
193
|
adantrl |
|
195 |
194
|
ad4ant23 |
|
196 |
|
simpll |
|
197 |
196
|
anim1i |
|
198 |
197
|
anim1i |
|
199 |
112 152
|
sstrdi |
|
200 |
199
|
adantr |
|
201 |
|
0re |
|
202 |
|
rpge0 |
|
203 |
202
|
rgen |
|
204 |
|
ssralv |
|
205 |
112 203 204
|
mpisyl |
|
206 |
|
breq1 |
|
207 |
206
|
ralbidv |
|
208 |
207
|
rspcev |
|
209 |
201 205 208
|
sylancr |
|
210 |
209
|
adantr |
|
211 |
145
|
adantr |
|
212 |
|
ffn |
|
213 |
|
fnfvelrn |
|
214 |
212 213
|
sylan |
|
215 |
|
2ndrn |
|
216 |
211 214 215
|
syl2anc |
|
217 |
|
infrelb |
|
218 |
200 210 216 217
|
syl3anc |
|
219 |
218
|
adantll |
|
220 |
219
|
ad2ant2r |
|
221 |
1
|
ad3antrrr |
|
222 |
|
xmetcl |
|
223 |
222
|
3expb |
|
224 |
221 223
|
sylan |
|
225 |
224
|
adantr |
|
226 |
|
simplr |
|
227 |
|
simpl |
|
228 |
216
|
ne0d |
|
229 |
|
infrecl |
|
230 |
200 228 210 229
|
syl3anc |
|
231 |
230
|
rexrd |
|
232 |
226 227 231
|
syl2an |
|
233 |
|
simpr |
|
234 |
233
|
ffvelrnda |
|
235 |
|
xp2nd |
|
236 |
234 235
|
syl |
|
237 |
236
|
rpxrd |
|
238 |
237
|
ad2ant2r |
|
239 |
|
xrltletr |
|
240 |
225 232 238 239
|
syl3anc |
|
241 |
220 240
|
mpan2d |
|
242 |
241
|
adantlr |
|
243 |
1
|
ad6antr |
|
244 |
|
simpllr |
|
245 |
|
ffvelrn |
|
246 |
|
xp1st |
|
247 |
245 246
|
syl |
|
248 |
244 227 247
|
syl2an |
|
249 |
|
simpr |
|
250 |
249
|
ad3antlr |
|
251 |
|
xmetcl |
|
252 |
243 248 250 251
|
syl3anc |
|
253 |
252
|
adantr |
|
254 |
245 235
|
syl |
|
255 |
226 254
|
sylan |
|
256 |
255
|
ad2ant2r |
|
257 |
256
|
rpred |
|
258 |
164
|
ad3antlr |
|
259 |
|
xmetcl |
|
260 |
243 248 258 259
|
syl3anc |
|
261 |
254
|
rpxrd |
|
262 |
244 227 261
|
syl2an |
|
263 |
|
eleq2 |
|
264 |
1
|
ad5antr |
|
265 |
226 247
|
sylan |
|
266 |
255
|
rpxrd |
|
267 |
|
elbl |
|
268 |
264 265 266 267
|
syl3anc |
|
269 |
263 268
|
sylan9bbr |
|
270 |
269
|
biimpd |
|
271 |
270
|
an32s |
|
272 |
271
|
impr |
|
273 |
272
|
simprd |
|
274 |
260 262 273
|
xrltled |
|
275 |
226
|
ffvelrnda |
|
276 |
275 246
|
syl |
|
277 |
|
simplrl |
|
278 |
264 276 277 259
|
syl3anc |
|
279 |
|
xmetge0 |
|
280 |
264 276 277 279
|
syl3anc |
|
281 |
|
xrrege0 |
|
282 |
281
|
an4s |
|
283 |
282
|
ex |
|
284 |
278 280 283
|
syl2anc |
|
285 |
284
|
ad2ant2r |
|
286 |
257 274 285
|
mp2and |
|
287 |
286
|
adantr |
|
288 |
|
xrltle |
|
289 |
225 238 288
|
syl2anc |
|
290 |
|
xmetge0 |
|
291 |
290
|
3expb |
|
292 |
221 291
|
sylan |
|
293 |
292
|
adantr |
|
294 |
236
|
rpred |
|
295 |
294
|
ad2ant2r |
|
296 |
|
xrrege0 |
|
297 |
296
|
ex |
|
298 |
225 295 297
|
syl2anc |
|
299 |
293 298
|
mpand |
|
300 |
289 299
|
syld |
|
301 |
300
|
adantlr |
|
302 |
301
|
imp |
|
303 |
287 302
|
readdcld |
|
304 |
303
|
rexrd |
|
305 |
256 256
|
rpaddcld |
|
306 |
305
|
rpxrd |
|
307 |
306
|
adantr |
|
308 |
|
xmettri |
|
309 |
243 248 250 258 308
|
syl13anc |
|
310 |
309
|
adantr |
|
311 |
|
rexadd |
|
312 |
287 302 311
|
syl2anc |
|
313 |
310 312
|
breqtrd |
|
314 |
257
|
adantr |
|
315 |
273
|
adantr |
|
316 |
|
simpr |
|
317 |
287 302 314 314 315 316
|
lt2addd |
|
318 |
253 304 307 313 317
|
xrlelttrd |
|
319 |
318
|
ex |
|
320 |
254
|
rpred |
|
321 |
320 254
|
ltaddrpd |
|
322 |
244 227 321
|
syl2an |
|
323 |
260 262 306 273 322
|
xrlttrd |
|
324 |
319 323
|
jctild |
|
325 |
242 324
|
syld |
|
326 |
|
simpll |
|
327 |
|
ffvelrn |
|
328 |
|
ffvelrn |
|
329 |
327 328
|
anim12dan |
|
330 |
|
xmetcl |
|
331 |
330
|
3expb |
|
332 |
2 329 331
|
syl2an |
|
333 |
332
|
anassrs |
|
334 |
326 333
|
sylan |
|
335 |
334
|
ad3antrrr |
|
336 |
2
|
ad5antr |
|
337 |
|
simp-5r |
|
338 |
337 276
|
ffvelrnd |
|
339 |
|
simpllr |
|
340 |
339
|
ffvelrnda |
|
341 |
340
|
adantrr |
|
342 |
341
|
adantr |
|
343 |
|
xmetcl |
|
344 |
336 338 342 343
|
syl3anc |
|
345 |
14
|
rpxrd |
|
346 |
345
|
ad4antlr |
|
347 |
|
xrltle |
|
348 |
344 346 347
|
syl2anc |
|
349 |
|
xmetge0 |
|
350 |
336 338 342 349
|
syl3anc |
|
351 |
14
|
rpred |
|
352 |
351
|
ad4antlr |
|
353 |
|
xrrege0 |
|
354 |
353
|
ex |
|
355 |
344 352 354
|
syl2anc |
|
356 |
350 355
|
mpand |
|
357 |
348 356
|
syld |
|
358 |
357
|
ad2ant2r |
|
359 |
358
|
imp |
|
360 |
339
|
ffvelrnda |
|
361 |
360
|
adantrl |
|
362 |
361
|
adantr |
|
363 |
|
xmetcl |
|
364 |
336 338 362 363
|
syl3anc |
|
365 |
|
xrltle |
|
366 |
364 346 365
|
syl2anc |
|
367 |
|
xmetge0 |
|
368 |
336 338 362 367
|
syl3anc |
|
369 |
|
xrrege0 |
|
370 |
369
|
ex |
|
371 |
364 352 370
|
syl2anc |
|
372 |
368 371
|
mpand |
|
373 |
366 372
|
syld |
|
374 |
373
|
ad2ant2r |
|
375 |
374
|
imp |
|
376 |
|
readdcl |
|
377 |
359 375 376
|
syl2an |
|
378 |
377
|
anandis |
|
379 |
378
|
rexrd |
|
380 |
|
rpxr |
|
381 |
380
|
ad6antlr |
|
382 |
|
xmettri |
|
383 |
336 342 362 338 382
|
syl13anc |
|
384 |
383
|
ad2ant2r |
|
385 |
384
|
adantr |
|
386 |
|
xmetsym |
|
387 |
336 342 338 386
|
syl3anc |
|
388 |
387
|
ad2ant2r |
|
389 |
388
|
adantr |
|
390 |
389
|
oveq1d |
|
391 |
|
rexadd |
|
392 |
359 375 391
|
syl2an |
|
393 |
392
|
anandis |
|
394 |
390 393
|
eqtrd |
|
395 |
385 394
|
breqtrd |
|
396 |
|
lt2add |
|
397 |
396
|
expcom |
|
398 |
352 352 397
|
syl2anc |
|
399 |
357 373 398
|
syl2and |
|
400 |
399
|
pm2.43d |
|
401 |
400
|
ad2ant2r |
|
402 |
401
|
imp |
|
403 |
|
rpcn |
|
404 |
403
|
2halvesd |
|
405 |
404
|
ad6antlr |
|
406 |
402 405
|
breqtrd |
|
407 |
335 379 381 395 406
|
xrlelttrd |
|
408 |
407
|
ex |
|
409 |
325 408
|
imim12d |
|
410 |
198 409
|
sylanl1 |
|
411 |
410
|
adantlrr |
|
412 |
195 411
|
mpd |
|
413 |
412
|
exp32 |
|
414 |
176 413
|
sylan2 |
|
415 |
414
|
expr |
|
416 |
415
|
pm2.43d |
|
417 |
416
|
an32s |
|
418 |
174 175 417
|
rexlimd |
|
419 |
169 418
|
mpd |
|
420 |
419
|
ralrimivva |
|
421 |
|
breq2 |
|
422 |
421
|
imbi1d |
|
423 |
422
|
2ralbidv |
|
424 |
423
|
rspcev |
|
425 |
160 420 424
|
syl2anc |
|
426 |
425
|
expl |
|
427 |
426
|
exlimdv |
|
428 |
427
|
expimpd |
|
429 |
105 428
|
sylan2 |
|
430 |
429
|
rexlimdva |
|
431 |
104 430
|
syld |
|
432 |
20 431
|
syl5 |
|
433 |
432
|
exp4b |
|
434 |
14 433
|
mpdi |
|
435 |
434
|
ralrimiv |
|
436 |
|
r19.21v |
|
437 |
435 436
|
sylib |
|
438 |
13 437
|
impbid2 |
|
439 |
|
ralcom |
|
440 |
438 439
|
bitrdi |
|
441 |
440
|
pm5.32da |
|
442 |
|
eqid |
|
443 |
|
eqid |
|
444 |
|
xmetpsmet |
|
445 |
1 444
|
syl |
|
446 |
|
xmetpsmet |
|
447 |
2 446
|
syl |
|
448 |
442 443 4 5 445 447
|
metucn |
|
449 |
|
eqid |
|
450 |
26 449
|
metcn |
|
451 |
1 2 450
|
syl2anc |
|
452 |
441 448 451
|
3bitr4d |
|
453 |
452
|
eqrdv |
|