Step |
Hyp |
Ref |
Expression |
1 |
|
poimir.0 |
|
2 |
|
poimirlem22.s |
|
3 |
|
poimirlem22.1 |
|
4 |
|
poimirlem22.2 |
|
5 |
|
poimirlem22.3 |
|
6 |
|
poimirlem21.4 |
|
7 |
|
oveq2 |
|
8 |
7
|
eleq1d |
|
9 |
|
oveq2 |
|
10 |
9
|
eleq1d |
|
11 |
|
fveq2 |
|
12 |
11
|
oveq1d |
|
13 |
12
|
adantl |
|
14 |
|
elrabi |
|
15 |
14 2
|
eleq2s |
|
16 |
4 15
|
syl |
|
17 |
|
xp1st |
|
18 |
16 17
|
syl |
|
19 |
|
xp1st |
|
20 |
18 19
|
syl |
|
21 |
|
elmapi |
|
22 |
20 21
|
syl |
|
23 |
|
xp2nd |
|
24 |
18 23
|
syl |
|
25 |
|
fvex |
|
26 |
|
f1oeq1 |
|
27 |
25 26
|
elab |
|
28 |
24 27
|
sylib |
|
29 |
|
f1of |
|
30 |
28 29
|
syl |
|
31 |
|
elfz1end |
|
32 |
1 31
|
sylib |
|
33 |
30 32
|
ffvelrnd |
|
34 |
22 33
|
ffvelrnd |
|
35 |
|
elfzonn0 |
|
36 |
34 35
|
syl |
|
37 |
|
fvex |
|
38 |
|
eleq1 |
|
39 |
38
|
anbi2d |
|
40 |
|
fveq2 |
|
41 |
40
|
neeq1d |
|
42 |
41
|
rexbidv |
|
43 |
39 42
|
imbi12d |
|
44 |
37 43 5
|
vtocl |
|
45 |
33 44
|
mpdan |
|
46 |
|
fveq1 |
|
47 |
22
|
ffnd |
|
48 |
47
|
adantr |
|
49 |
|
1ex |
|
50 |
|
fnconstg |
|
51 |
49 50
|
ax-mp |
|
52 |
|
c0ex |
|
53 |
|
fnconstg |
|
54 |
52 53
|
ax-mp |
|
55 |
51 54
|
pm3.2i |
|
56 |
|
dff1o3 |
|
57 |
56
|
simprbi |
|
58 |
28 57
|
syl |
|
59 |
|
imain |
|
60 |
58 59
|
syl |
|
61 |
|
elfznn0 |
|
62 |
61
|
nn0red |
|
63 |
62
|
ltp1d |
|
64 |
|
fzdisj |
|
65 |
63 64
|
syl |
|
66 |
65
|
imaeq2d |
|
67 |
|
ima0 |
|
68 |
66 67
|
eqtrdi |
|
69 |
60 68
|
sylan9req |
|
70 |
|
fnun |
|
71 |
55 69 70
|
sylancr |
|
72 |
|
imaundi |
|
73 |
|
nn0p1nn |
|
74 |
|
nnuz |
|
75 |
73 74
|
eleqtrdi |
|
76 |
61 75
|
syl |
|
77 |
76
|
adantl |
|
78 |
1
|
nncnd |
|
79 |
|
npcan1 |
|
80 |
78 79
|
syl |
|
81 |
80
|
adantr |
|
82 |
|
elfzuz3 |
|
83 |
|
peano2uz |
|
84 |
82 83
|
syl |
|
85 |
84
|
adantl |
|
86 |
81 85
|
eqeltrrd |
|
87 |
|
fzsplit2 |
|
88 |
77 86 87
|
syl2anc |
|
89 |
88
|
imaeq2d |
|
90 |
|
f1ofo |
|
91 |
|
foima |
|
92 |
28 90 91
|
3syl |
|
93 |
92
|
adantr |
|
94 |
89 93
|
eqtr3d |
|
95 |
72 94
|
eqtr3id |
|
96 |
95
|
fneq2d |
|
97 |
71 96
|
mpbid |
|
98 |
|
ovex |
|
99 |
98
|
a1i |
|
100 |
|
inidm |
|
101 |
|
eqidd |
|
102 |
|
f1ofn |
|
103 |
28 102
|
syl |
|
104 |
103
|
adantr |
|
105 |
|
fzss1 |
|
106 |
76 105
|
syl |
|
107 |
106
|
adantl |
|
108 |
|
eluzp1p1 |
|
109 |
|
uzss |
|
110 |
82 108 109
|
3syl |
|
111 |
110
|
adantl |
|
112 |
1
|
nnzd |
|
113 |
112
|
uzidd |
|
114 |
80
|
fveq2d |
|
115 |
113 114
|
eleqtrrd |
|
116 |
115
|
adantr |
|
117 |
111 116
|
sseldd |
|
118 |
|
eluzfz2 |
|
119 |
117 118
|
syl |
|
120 |
|
fnfvima |
|
121 |
104 107 119 120
|
syl3anc |
|
122 |
|
fvun2 |
|
123 |
51 54 122
|
mp3an12 |
|
124 |
69 121 123
|
syl2anc |
|
125 |
52
|
fvconst2 |
|
126 |
121 125
|
syl |
|
127 |
124 126
|
eqtrd |
|
128 |
127
|
adantr |
|
129 |
48 97 99 99 100 101 128
|
ofval |
|
130 |
33 129
|
mpidan |
|
131 |
36
|
nn0cnd |
|
132 |
131
|
addid1d |
|
133 |
132
|
adantr |
|
134 |
130 133
|
eqtrd |
|
135 |
46 134
|
sylan9eqr |
|
136 |
135
|
adantllr |
|
137 |
|
fveq2 |
|
138 |
137
|
breq2d |
|
139 |
138
|
ifbid |
|
140 |
|
2fveq3 |
|
141 |
|
2fveq3 |
|
142 |
141
|
imaeq1d |
|
143 |
142
|
xpeq1d |
|
144 |
141
|
imaeq1d |
|
145 |
144
|
xpeq1d |
|
146 |
143 145
|
uneq12d |
|
147 |
140 146
|
oveq12d |
|
148 |
139 147
|
csbeq12dv |
|
149 |
148
|
mpteq2dv |
|
150 |
149
|
eqeq2d |
|
151 |
150 2
|
elrab2 |
|
152 |
151
|
simprbi |
|
153 |
4 152
|
syl |
|
154 |
62
|
adantl |
|
155 |
|
peano2zm |
|
156 |
112 155
|
syl |
|
157 |
156
|
zred |
|
158 |
157
|
adantr |
|
159 |
1
|
nnred |
|
160 |
159
|
adantr |
|
161 |
|
elfzle2 |
|
162 |
161
|
adantl |
|
163 |
159
|
ltm1d |
|
164 |
163
|
adantr |
|
165 |
154 158 160 162 164
|
lelttrd |
|
166 |
6
|
adantr |
|
167 |
165 166
|
breqtrrd |
|
168 |
167
|
iftrued |
|
169 |
168
|
csbeq1d |
|
170 |
|
vex |
|
171 |
|
oveq2 |
|
172 |
171
|
imaeq2d |
|
173 |
172
|
xpeq1d |
|
174 |
|
oveq1 |
|
175 |
174
|
oveq1d |
|
176 |
175
|
imaeq2d |
|
177 |
176
|
xpeq1d |
|
178 |
173 177
|
uneq12d |
|
179 |
178
|
oveq2d |
|
180 |
170 179
|
csbie |
|
181 |
169 180
|
eqtrdi |
|
182 |
181
|
mpteq2dva |
|
183 |
153 182
|
eqtrd |
|
184 |
183
|
rneqd |
|
185 |
184
|
eleq2d |
|
186 |
|
eqid |
|
187 |
|
ovex |
|
188 |
186 187
|
elrnmpti |
|
189 |
185 188
|
bitrdi |
|
190 |
189
|
biimpa |
|
191 |
136 190
|
r19.29a |
|
192 |
191
|
neeq1d |
|
193 |
192
|
biimpd |
|
194 |
193
|
rexlimdva |
|
195 |
45 194
|
mpd |
|
196 |
|
elnnne0 |
|
197 |
36 195 196
|
sylanbrc |
|
198 |
|
nnm1nn0 |
|
199 |
197 198
|
syl |
|
200 |
|
elfzo0 |
|
201 |
34 200
|
sylib |
|
202 |
201
|
simp2d |
|
203 |
199
|
nn0red |
|
204 |
36
|
nn0red |
|
205 |
202
|
nnred |
|
206 |
204
|
ltm1d |
|
207 |
|
elfzolt2 |
|
208 |
34 207
|
syl |
|
209 |
203 204 205 206 208
|
lttrd |
|
210 |
|
elfzo0 |
|
211 |
199 202 209 210
|
syl3anbrc |
|
212 |
211
|
adantr |
|
213 |
13 212
|
eqeltrd |
|
214 |
213
|
adantlr |
|
215 |
22
|
ffvelrnda |
|
216 |
|
elfzonn0 |
|
217 |
215 216
|
syl |
|
218 |
217
|
nn0cnd |
|
219 |
218
|
subid1d |
|
220 |
219 215
|
eqeltrd |
|
221 |
220
|
adantr |
|
222 |
8 10 214 221
|
ifbothda |
|
223 |
222
|
fmpttd |
|
224 |
|
ovex |
|
225 |
224 98
|
elmap |
|
226 |
223 225
|
sylibr |
|
227 |
|
simpr |
|
228 |
|
1z |
|
229 |
|
peano2z |
|
230 |
228 229
|
ax-mp |
|
231 |
112 230
|
jctil |
|
232 |
|
elfzelz |
|
233 |
232 228
|
jctir |
|
234 |
|
fzsubel |
|
235 |
231 233 234
|
syl2an |
|
236 |
227 235
|
mpbid |
|
237 |
|
ax-1cn |
|
238 |
237 237
|
pncan3oi |
|
239 |
238
|
oveq1i |
|
240 |
236 239
|
eleqtrdi |
|
241 |
240
|
ralrimiva |
|
242 |
|
simpr |
|
243 |
156 228
|
jctil |
|
244 |
|
elfzelz |
|
245 |
244 228
|
jctir |
|
246 |
|
fzaddel |
|
247 |
243 245 246
|
syl2an |
|
248 |
242 247
|
mpbid |
|
249 |
80
|
oveq2d |
|
250 |
249
|
adantr |
|
251 |
248 250
|
eleqtrd |
|
252 |
232
|
zcnd |
|
253 |
244
|
zcnd |
|
254 |
|
subadd2 |
|
255 |
237 254
|
mp3an2 |
|
256 |
|
eqcom |
|
257 |
|
eqcom |
|
258 |
255 256 257
|
3bitr4g |
|
259 |
252 253 258
|
syl2anr |
|
260 |
259
|
ralrimiva |
|
261 |
260
|
adantl |
|
262 |
|
reu6i |
|
263 |
251 261 262
|
syl2anc |
|
264 |
263
|
ralrimiva |
|
265 |
|
eqid |
|
266 |
265
|
f1ompt |
|
267 |
241 264 266
|
sylanbrc |
|
268 |
|
f1osng |
|
269 |
49 1 268
|
sylancr |
|
270 |
157 159
|
ltnled |
|
271 |
163 270
|
mpbid |
|
272 |
|
elfzle2 |
|
273 |
271 272
|
nsyl |
|
274 |
|
disjsn |
|
275 |
273 274
|
sylibr |
|
276 |
|
1re |
|
277 |
276
|
ltp1i |
|
278 |
230
|
zrei |
|
279 |
276 278
|
ltnlei |
|
280 |
277 279
|
mpbi |
|
281 |
|
elfzle1 |
|
282 |
280 281
|
mto |
|
283 |
|
disjsn |
|
284 |
282 283
|
mpbir |
|
285 |
|
f1oun |
|
286 |
284 285
|
mpanr1 |
|
287 |
267 269 275 286
|
syl21anc |
|
288 |
|
eleq1 |
|
289 |
282 288
|
mtbiri |
|
290 |
289
|
necon2ai |
|
291 |
|
ifnefalse |
|
292 |
290 291
|
syl |
|
293 |
292
|
mpteq2ia |
|
294 |
293
|
uneq1i |
|
295 |
49
|
a1i |
|
296 |
1 74
|
eleqtrdi |
|
297 |
|
fzpred |
|
298 |
296 297
|
syl |
|
299 |
|
uncom |
|
300 |
298 299
|
eqtr2di |
|
301 |
|
iftrue |
|
302 |
301
|
adantl |
|
303 |
295 1 300 302
|
fmptapd |
|
304 |
294 303
|
eqtr3id |
|
305 |
80 296
|
eqeltrd |
|
306 |
|
uzid |
|
307 |
|
peano2uz |
|
308 |
156 306 307
|
3syl |
|
309 |
80 308
|
eqeltrrd |
|
310 |
|
fzsplit2 |
|
311 |
305 309 310
|
syl2anc |
|
312 |
80
|
oveq1d |
|
313 |
|
fzsn |
|
314 |
112 313
|
syl |
|
315 |
312 314
|
eqtrd |
|
316 |
315
|
uneq2d |
|
317 |
311 316
|
eqtr2d |
|
318 |
304 300 317
|
f1oeq123d |
|
319 |
287 318
|
mpbid |
|
320 |
|
f1oco |
|
321 |
28 319 320
|
syl2anc |
|
322 |
98
|
mptex |
|
323 |
25 322
|
coex |
|
324 |
|
f1oeq1 |
|
325 |
323 324
|
elab |
|
326 |
321 325
|
sylibr |
|
327 |
226 326
|
opelxpd |
|
328 |
1
|
nnnn0d |
|
329 |
|
0elfz |
|
330 |
328 329
|
syl |
|
331 |
327 330
|
opelxpd |
|
332 |
1 2 3 4 5 6
|
poimirlem19 |
|
333 |
|
elfzle1 |
|
334 |
|
0re |
|
335 |
|
lenlt |
|
336 |
334 62 335
|
sylancr |
|
337 |
333 336
|
mpbid |
|
338 |
337
|
iffalsed |
|
339 |
338
|
csbeq1d |
|
340 |
|
ovex |
|
341 |
|
oveq2 |
|
342 |
341
|
imaeq2d |
|
343 |
342
|
xpeq1d |
|
344 |
|
oveq1 |
|
345 |
344
|
oveq1d |
|
346 |
345
|
imaeq2d |
|
347 |
346
|
xpeq1d |
|
348 |
343 347
|
uneq12d |
|
349 |
348
|
oveq2d |
|
350 |
340 349
|
csbie |
|
351 |
339 350
|
eqtrdi |
|
352 |
351
|
mpteq2ia |
|
353 |
332 352
|
eqtr4di |
|
354 |
|
opex |
|
355 |
354 52
|
op2ndd |
|
356 |
355
|
breq2d |
|
357 |
356
|
ifbid |
|
358 |
354 52
|
op1std |
|
359 |
98
|
mptex |
|
360 |
359 323
|
op1std |
|
361 |
358 360
|
syl |
|
362 |
359 323
|
op2ndd |
|
363 |
358 362
|
syl |
|
364 |
363
|
imaeq1d |
|
365 |
364
|
xpeq1d |
|
366 |
363
|
imaeq1d |
|
367 |
366
|
xpeq1d |
|
368 |
365 367
|
uneq12d |
|
369 |
361 368
|
oveq12d |
|
370 |
357 369
|
csbeq12dv |
|
371 |
370
|
mpteq2dv |
|
372 |
371
|
eqeq2d |
|
373 |
372 2
|
elrab2 |
|
374 |
331 353 373
|
sylanbrc |
|
375 |
354 52
|
op2ndd |
|
376 |
375
|
eqcoms |
|
377 |
1
|
nnne0d |
|
378 |
377
|
necomd |
|
379 |
|
neeq1 |
|
380 |
378 379
|
syl5ibrcom |
|
381 |
376 380
|
syl5 |
|
382 |
381
|
necon2d |
|
383 |
6 382
|
mpd |
|
384 |
|
neeq1 |
|
385 |
384
|
rspcev |
|
386 |
374 383 385
|
syl2anc |
|