Step |
Hyp |
Ref |
Expression |
1 |
|
poimir.0 |
|
2 |
|
poimirlem23.1 |
|
3 |
|
poimirlem23.2 |
|
4 |
|
poimirlem23.3 |
|
5 |
|
ovex |
|
6 |
5
|
csbex |
|
7 |
6
|
rgenw |
|
8 |
|
eqid |
|
9 |
|
fveq1 |
|
10 |
9
|
neeq1d |
|
11 |
|
df-ne |
|
12 |
10 11
|
syl6bb |
|
13 |
8 12
|
rexrnmptw |
|
14 |
7 13
|
ax-mp |
|
15 |
|
rexnal |
|
16 |
14 15
|
bitri |
|
17 |
1
|
nnzd |
|
18 |
|
elfzelz |
|
19 |
4 18
|
syl |
|
20 |
|
zlem1lt |
|
21 |
17 19 20
|
syl2anc |
|
22 |
|
elfzle2 |
|
23 |
4 22
|
syl |
|
24 |
19
|
zred |
|
25 |
1
|
nnred |
|
26 |
24 25
|
letri3d |
|
27 |
26
|
biimprd |
|
28 |
23 27
|
mpand |
|
29 |
21 28
|
sylbird |
|
30 |
29
|
necon3ad |
|
31 |
|
nnm1nn0 |
|
32 |
1 31
|
syl |
|
33 |
|
nn0fz0 |
|
34 |
32 33
|
sylib |
|
35 |
34
|
adantr |
|
36 |
|
iffalse |
|
37 |
1
|
nncnd |
|
38 |
|
npcan1 |
|
39 |
37 38
|
syl |
|
40 |
36 39
|
sylan9eqr |
|
41 |
40
|
csbeq1d |
|
42 |
|
oveq2 |
|
43 |
42
|
imaeq2d |
|
44 |
43
|
xpeq1d |
|
45 |
|
oveq1 |
|
46 |
45
|
oveq1d |
|
47 |
46
|
imaeq2d |
|
48 |
47
|
xpeq1d |
|
49 |
44 48
|
uneq12d |
|
50 |
|
f1ofo |
|
51 |
|
foima |
|
52 |
3 50 51
|
3syl |
|
53 |
52
|
xpeq1d |
|
54 |
25
|
ltp1d |
|
55 |
17
|
peano2zd |
|
56 |
|
fzn |
|
57 |
55 17 56
|
syl2anc |
|
58 |
54 57
|
mpbid |
|
59 |
58
|
imaeq2d |
|
60 |
59
|
xpeq1d |
|
61 |
|
ima0 |
|
62 |
61
|
xpeq1i |
|
63 |
|
0xp |
|
64 |
62 63
|
eqtri |
|
65 |
60 64
|
eqtrdi |
|
66 |
53 65
|
uneq12d |
|
67 |
|
un0 |
|
68 |
66 67
|
eqtrdi |
|
69 |
49 68
|
sylan9eqr |
|
70 |
69
|
oveq2d |
|
71 |
1 70
|
csbied |
|
72 |
71
|
adantr |
|
73 |
41 72
|
eqtrd |
|
74 |
73
|
fveq1d |
|
75 |
|
elfzonn0 |
|
76 |
|
nn0p1nn |
|
77 |
75 76
|
syl |
|
78 |
|
elsni |
|
79 |
78
|
oveq2d |
|
80 |
79
|
eleq1d |
|
81 |
77 80
|
syl5ibrcom |
|
82 |
81
|
imp |
|
83 |
82
|
adantl |
|
84 |
|
1ex |
|
85 |
84
|
fconst |
|
86 |
85
|
a1i |
|
87 |
|
ovexd |
|
88 |
|
inidm |
|
89 |
83 2 86 87 87 88
|
off |
|
90 |
|
elfz1end |
|
91 |
1 90
|
sylib |
|
92 |
89 91
|
ffvelrnd |
|
93 |
92
|
adantr |
|
94 |
74 93
|
eqeltrd |
|
95 |
94
|
nnne0d |
|
96 |
|
breq1 |
|
97 |
|
id |
|
98 |
|
oveq1 |
|
99 |
96 97 98
|
ifbieq12d |
|
100 |
99
|
csbeq1d |
|
101 |
100
|
fveq1d |
|
102 |
101
|
neeq1d |
|
103 |
11 102
|
bitr3id |
|
104 |
103
|
rspcev |
|
105 |
35 95 104
|
syl2anc |
|
106 |
105 15
|
sylib |
|
107 |
106
|
ex |
|
108 |
30 107
|
syld |
|
109 |
108
|
necon4ad |
|
110 |
109
|
pm4.71rd |
|
111 |
32
|
nn0zd |
|
112 |
|
uzid |
|
113 |
|
peano2uz |
|
114 |
111 112 113
|
3syl |
|
115 |
39 114
|
eqeltrrd |
|
116 |
|
fzss2 |
|
117 |
115 116
|
syl |
|
118 |
117
|
sselda |
|
119 |
91
|
adantr |
|
120 |
2
|
ffnd |
|
121 |
120
|
adantr |
|
122 |
84
|
fconst |
|
123 |
|
c0ex |
|
124 |
123
|
fconst |
|
125 |
122 124
|
pm3.2i |
|
126 |
|
dff1o3 |
|
127 |
126
|
simprbi |
|
128 |
|
imain |
|
129 |
3 127 128
|
3syl |
|
130 |
|
elfzelz |
|
131 |
130
|
zred |
|
132 |
131
|
ltp1d |
|
133 |
|
fzdisj |
|
134 |
132 133
|
syl |
|
135 |
134
|
imaeq2d |
|
136 |
135 61
|
eqtrdi |
|
137 |
129 136
|
sylan9req |
|
138 |
|
fun |
|
139 |
125 137 138
|
sylancr |
|
140 |
|
elfznn0 |
|
141 |
140 76
|
syl |
|
142 |
|
nnuz |
|
143 |
141 142
|
eleqtrdi |
|
144 |
|
elfzuz3 |
|
145 |
|
fzsplit2 |
|
146 |
143 144 145
|
syl2anc |
|
147 |
146
|
imaeq2d |
|
148 |
|
imaundi |
|
149 |
147 148
|
eqtr2di |
|
150 |
149 52
|
sylan9eqr |
|
151 |
150
|
feq2d |
|
152 |
139 151
|
mpbid |
|
153 |
152
|
ffnd |
|
154 |
|
ovexd |
|
155 |
|
eqidd |
|
156 |
|
eqidd |
|
157 |
121 153 154 154 88 155 156
|
ofval |
|
158 |
119 157
|
mpdan |
|
159 |
158
|
eqeq1d |
|
160 |
2 91
|
ffvelrnd |
|
161 |
|
elfzonn0 |
|
162 |
160 161
|
syl |
|
163 |
162
|
nn0red |
|
164 |
163
|
adantr |
|
165 |
162
|
nn0ge0d |
|
166 |
165
|
adantr |
|
167 |
|
1re |
|
168 |
|
snssi |
|
169 |
167 168
|
ax-mp |
|
170 |
|
0re |
|
171 |
|
snssi |
|
172 |
170 171
|
ax-mp |
|
173 |
169 172
|
unssi |
|
174 |
152 119
|
ffvelrnd |
|
175 |
173 174
|
sseldi |
|
176 |
|
elun |
|
177 |
|
0le1 |
|
178 |
|
elsni |
|
179 |
177 178
|
breqtrrid |
|
180 |
|
0le0 |
|
181 |
|
elsni |
|
182 |
180 181
|
breqtrrid |
|
183 |
179 182
|
jaoi |
|
184 |
176 183
|
sylbi |
|
185 |
174 184
|
syl |
|
186 |
|
add20 |
|
187 |
164 166 175 185 186
|
syl22anc |
|
188 |
159 187
|
bitrd |
|
189 |
118 188
|
syldan |
|
190 |
189
|
ralbidva |
|
191 |
190
|
adantr |
|
192 |
|
breq2 |
|
193 |
192
|
ifbid |
|
194 |
|
elfzelz |
|
195 |
194
|
zred |
|
196 |
195
|
adantl |
|
197 |
32
|
nn0red |
|
198 |
197
|
adantr |
|
199 |
25
|
adantr |
|
200 |
|
elfzle2 |
|
201 |
200
|
adantl |
|
202 |
25
|
ltm1d |
|
203 |
202
|
adantr |
|
204 |
196 198 199 201 203
|
lelttrd |
|
205 |
204
|
iftrued |
|
206 |
193 205
|
sylan9eqr |
|
207 |
206
|
an32s |
|
208 |
207
|
csbeq1d |
|
209 |
208
|
fveq1d |
|
210 |
209
|
eqeq1d |
|
211 |
210
|
ralbidva |
|
212 |
|
nfv |
|
213 |
|
nfcsb1v |
|
214 |
|
nfcv |
|
215 |
213 214
|
nffv |
|
216 |
215
|
nfeq1 |
|
217 |
|
csbeq1a |
|
218 |
217
|
fveq1d |
|
219 |
218
|
eqeq1d |
|
220 |
212 216 219
|
cbvralw |
|
221 |
211 220
|
bitr4di |
|
222 |
|
ne0i |
|
223 |
|
r19.3rzv |
|
224 |
34 222 223
|
3syl |
|
225 |
|
elfzelz |
|
226 |
225
|
zred |
|
227 |
226
|
ltp1d |
|
228 |
227 133
|
syl |
|
229 |
228
|
imaeq2d |
|
230 |
229 61
|
eqtrdi |
|
231 |
129 230
|
sylan9req |
|
232 |
231
|
adantlr |
|
233 |
|
simplr |
|
234 |
|
f1ofn |
|
235 |
3 234
|
syl |
|
236 |
235
|
adantr |
|
237 |
|
elfznn0 |
|
238 |
237 76
|
syl |
|
239 |
238 142
|
eleqtrdi |
|
240 |
|
fzss1 |
|
241 |
239 240
|
syl |
|
242 |
241
|
adantl |
|
243 |
39
|
adantr |
|
244 |
|
elfzuz3 |
|
245 |
|
eluzp1p1 |
|
246 |
244 245
|
syl |
|
247 |
246
|
adantl |
|
248 |
243 247
|
eqeltrrd |
|
249 |
|
eluzfz2 |
|
250 |
248 249
|
syl |
|
251 |
|
fnfvima |
|
252 |
236 242 250 251
|
syl3anc |
|
253 |
252
|
adantlr |
|
254 |
233 253
|
eqeltrrd |
|
255 |
|
fnconstg |
|
256 |
84 255
|
ax-mp |
|
257 |
|
fnconstg |
|
258 |
123 257
|
ax-mp |
|
259 |
|
fvun2 |
|
260 |
256 258 259
|
mp3an12 |
|
261 |
232 254 260
|
syl2anc |
|
262 |
123
|
fvconst2 |
|
263 |
254 262
|
syl |
|
264 |
261 263
|
eqtrd |
|
265 |
264
|
ralrimiva |
|
266 |
265
|
ex |
|
267 |
34
|
adantr |
|
268 |
|
ax-1ne0 |
|
269 |
|
imain |
|
270 |
3 127 269
|
3syl |
|
271 |
202 39
|
breqtrrd |
|
272 |
|
fzdisj |
|
273 |
271 272
|
syl |
|
274 |
273
|
imaeq2d |
|
275 |
274 61
|
eqtrdi |
|
276 |
270 275
|
eqtr3d |
|
277 |
276
|
adantr |
|
278 |
91
|
adantr |
|
279 |
|
elimasni |
|
280 |
|
fnbrfvb |
|
281 |
235 91 280
|
syl2anc |
|
282 |
279 281
|
syl5ibr |
|
283 |
282
|
necon3ad |
|
284 |
283
|
imp |
|
285 |
278 284
|
eldifd |
|
286 |
|
imadif |
|
287 |
3 127 286
|
3syl |
|
288 |
|
difun2 |
|
289 |
|
elun |
|
290 |
|
velsn |
|
291 |
290
|
orbi2i |
|
292 |
289 291
|
bitri |
|
293 |
1 142
|
eleqtrdi |
|
294 |
|
fzm1 |
|
295 |
293 294
|
syl |
|
296 |
292 295
|
bitr4id |
|
297 |
296
|
eqrdv |
|
298 |
297
|
difeq1d |
|
299 |
197 25
|
ltnled |
|
300 |
202 299
|
mpbid |
|
301 |
|
elfzle2 |
|
302 |
300 301
|
nsyl |
|
303 |
|
difsn |
|
304 |
302 303
|
syl |
|
305 |
288 298 304
|
3eqtr3a |
|
306 |
305
|
imaeq2d |
|
307 |
52
|
difeq1d |
|
308 |
287 306 307
|
3eqtr3rd |
|
309 |
308
|
adantr |
|
310 |
285 309
|
eleqtrd |
|
311 |
|
fnconstg |
|
312 |
84 311
|
ax-mp |
|
313 |
|
fnconstg |
|
314 |
123 313
|
ax-mp |
|
315 |
|
fvun1 |
|
316 |
312 314 315
|
mp3an12 |
|
317 |
277 310 316
|
syl2anc |
|
318 |
84
|
fvconst2 |
|
319 |
310 318
|
syl |
|
320 |
317 319
|
eqtrd |
|
321 |
320
|
neeq1d |
|
322 |
268 321
|
mpbiri |
|
323 |
|
df-ne |
|
324 |
|
oveq2 |
|
325 |
324
|
imaeq2d |
|
326 |
325
|
xpeq1d |
|
327 |
|
oveq1 |
|
328 |
327
|
oveq1d |
|
329 |
328
|
imaeq2d |
|
330 |
329
|
xpeq1d |
|
331 |
326 330
|
uneq12d |
|
332 |
331
|
fveq1d |
|
333 |
332
|
neeq1d |
|
334 |
323 333
|
bitr3id |
|
335 |
334
|
rspcev |
|
336 |
267 322 335
|
syl2anc |
|
337 |
336
|
ex |
|
338 |
|
rexnal |
|
339 |
337 338
|
syl6ib |
|
340 |
339
|
necon4ad |
|
341 |
266 340
|
impbid |
|
342 |
224 341
|
anbi12d |
|
343 |
|
r19.26 |
|
344 |
342 343
|
bitr4di |
|
345 |
344
|
adantr |
|
346 |
191 221 345
|
3bitr4d |
|
347 |
346
|
pm5.32da |
|
348 |
110 347
|
bitrd |
|
349 |
348
|
notbid |
|
350 |
16 349
|
syl5bb |
|