Step |
Hyp |
Ref |
Expression |
1 |
|
poimir.0 |
|
2 |
|
poimirlem28.1 |
|
3 |
|
poimirlem28.2 |
|
4 |
|
poimirlem25.3 |
|
5 |
|
poimirlem25.4 |
|
6 |
|
poimirlem24.5 |
|
7 |
|
nfv |
|
8 |
|
nfcsb1v |
|
9 |
|
nfcv |
|
10 |
|
nfcv |
|
11 |
8 9 10
|
nff |
|
12 |
7 11
|
nfim |
|
13 |
|
eleq1 |
|
14 |
13
|
anbi2d |
|
15 |
|
csbeq1a |
|
16 |
15
|
feq1d |
|
17 |
14 16
|
imbi12d |
|
18 |
1
|
nncnd |
|
19 |
|
npcan1 |
|
20 |
18 19
|
syl |
|
21 |
1
|
nnzd |
|
22 |
|
peano2zm |
|
23 |
21 22
|
syl |
|
24 |
|
uzid |
|
25 |
|
peano2uz |
|
26 |
23 24 25
|
3syl |
|
27 |
20 26
|
eqeltrrd |
|
28 |
|
fzss2 |
|
29 |
27 28
|
syl |
|
30 |
29
|
sselda |
|
31 |
|
elun |
|
32 |
|
fzofzp1 |
|
33 |
|
elsni |
|
34 |
33
|
oveq2d |
|
35 |
34
|
eleq1d |
|
36 |
32 35
|
syl5ibrcom |
|
37 |
|
elfzoelz |
|
38 |
37
|
zcnd |
|
39 |
38
|
addid1d |
|
40 |
|
elfzofz |
|
41 |
39 40
|
eqeltrd |
|
42 |
|
elsni |
|
43 |
42
|
oveq2d |
|
44 |
43
|
eleq1d |
|
45 |
41 44
|
syl5ibrcom |
|
46 |
36 45
|
jaod |
|
47 |
31 46
|
syl5bi |
|
48 |
47
|
imp |
|
49 |
48
|
adantl |
|
50 |
4
|
adantr |
|
51 |
|
1ex |
|
52 |
51
|
fconst |
|
53 |
|
c0ex |
|
54 |
53
|
fconst |
|
55 |
52 54
|
pm3.2i |
|
56 |
|
dff1o3 |
|
57 |
56
|
simprbi |
|
58 |
|
imain |
|
59 |
5 57 58
|
3syl |
|
60 |
|
elfznn0 |
|
61 |
60
|
nn0red |
|
62 |
61
|
ltp1d |
|
63 |
|
fzdisj |
|
64 |
62 63
|
syl |
|
65 |
64
|
imaeq2d |
|
66 |
|
ima0 |
|
67 |
65 66
|
eqtrdi |
|
68 |
59 67
|
sylan9req |
|
69 |
|
fun |
|
70 |
55 68 69
|
sylancr |
|
71 |
|
nn0p1nn |
|
72 |
60 71
|
syl |
|
73 |
|
nnuz |
|
74 |
72 73
|
eleqtrdi |
|
75 |
|
elfzuz3 |
|
76 |
|
fzsplit2 |
|
77 |
74 75 76
|
syl2anc |
|
78 |
77
|
imaeq2d |
|
79 |
|
imaundi |
|
80 |
78 79
|
eqtr2di |
|
81 |
|
f1ofo |
|
82 |
|
foima |
|
83 |
5 81 82
|
3syl |
|
84 |
80 83
|
sylan9eqr |
|
85 |
84
|
feq2d |
|
86 |
70 85
|
mpbid |
|
87 |
|
ovex |
|
88 |
87
|
a1i |
|
89 |
|
inidm |
|
90 |
49 50 86 88 88 89
|
off |
|
91 |
30 90
|
syldan |
|
92 |
12 17 91
|
chvarfv |
|
93 |
|
fzp1elp1 |
|
94 |
20
|
oveq2d |
|
95 |
94
|
eleq2d |
|
96 |
95
|
biimpa |
|
97 |
93 96
|
sylan2 |
|
98 |
|
nfv |
|
99 |
|
nfcsb1v |
|
100 |
99 9 10
|
nff |
|
101 |
98 100
|
nfim |
|
102 |
|
ovex |
|
103 |
|
eleq1 |
|
104 |
103
|
anbi2d |
|
105 |
|
csbeq1a |
|
106 |
105
|
feq1d |
|
107 |
104 106
|
imbi12d |
|
108 |
101 102 107 90
|
vtoclf |
|
109 |
97 108
|
syldan |
|
110 |
|
csbeq1 |
|
111 |
110
|
feq1d |
|
112 |
|
csbeq1 |
|
113 |
112
|
feq1d |
|
114 |
111 113
|
ifboth |
|
115 |
92 109 114
|
syl2anc |
|
116 |
|
ovex |
|
117 |
116 87
|
elmap |
|
118 |
115 117
|
sylibr |
|
119 |
118
|
fmpttd |
|
120 |
|
ovex |
|
121 |
|
ovex |
|
122 |
120 121
|
elmap |
|
123 |
119 122
|
sylibr |
|
124 |
|
rneq |
|
125 |
124
|
mpteq1d |
|
126 |
125
|
rneqd |
|
127 |
126
|
sseq2d |
|
128 |
124
|
rexeqdv |
|
129 |
127 128
|
anbi12d |
|
130 |
129
|
ceqsrexv |
|
131 |
123 130
|
syl |
|
132 |
|
dfss3 |
|
133 |
|
ovex |
|
134 |
133 2
|
csbie |
|
135 |
134
|
csbeq2i |
|
136 |
|
opex |
|
137 |
136
|
a1i |
|
138 |
|
fveq2 |
|
139 |
|
fex |
|
140 |
4 87 139
|
sylancl |
|
141 |
|
f1oexrnex |
|
142 |
5 87 141
|
sylancl |
|
143 |
|
op1stg |
|
144 |
140 142 143
|
syl2anc |
|
145 |
138 144
|
sylan9eqr |
|
146 |
|
fveq2 |
|
147 |
|
op2ndg |
|
148 |
140 142 147
|
syl2anc |
|
149 |
146 148
|
sylan9eqr |
|
150 |
|
imaeq1 |
|
151 |
150
|
xpeq1d |
|
152 |
|
imaeq1 |
|
153 |
152
|
xpeq1d |
|
154 |
151 153
|
uneq12d |
|
155 |
149 154
|
syl |
|
156 |
145 155
|
oveq12d |
|
157 |
156
|
csbeq1d |
|
158 |
137 157
|
csbied |
|
159 |
135 158
|
eqtr3id |
|
160 |
159
|
csbeq2dv |
|
161 |
160
|
eqeq2d |
|
162 |
161
|
rexbidv |
|
163 |
|
vex |
|
164 |
|
eqid |
|
165 |
164
|
elrnmpt |
|
166 |
163 165
|
ax-mp |
|
167 |
|
nfv |
|
168 |
|
nfcsb1v |
|
169 |
168
|
nfeq2 |
|
170 |
|
csbeq1a |
|
171 |
170
|
eqeq2d |
|
172 |
167 169 171
|
cbvrexw |
|
173 |
|
ovex |
|
174 |
173
|
csbex |
|
175 |
174
|
rgenw |
|
176 |
|
eqid |
|
177 |
|
csbeq1 |
|
178 |
|
vex |
|
179 |
178 102
|
ifex |
|
180 |
|
csbnestgw |
|
181 |
179 180
|
ax-mp |
|
182 |
177 181
|
eqtr4di |
|
183 |
182
|
eqeq2d |
|
184 |
176 183
|
rexrnmptw |
|
185 |
175 184
|
ax-mp |
|
186 |
166 172 185
|
3bitri |
|
187 |
162 186
|
bitr4di |
|
188 |
29
|
sselda |
|
189 |
188
|
adantr |
|
190 |
|
elfzelz |
|
191 |
190
|
zred |
|
192 |
191
|
adantl |
|
193 |
|
ltne |
|
194 |
193
|
necomd |
|
195 |
192 194
|
sylan |
|
196 |
|
eldifsn |
|
197 |
189 195 196
|
sylanbrc |
|
198 |
97
|
adantr |
|
199 |
6
|
elfzelzd |
|
200 |
199
|
zred |
|
201 |
200
|
ad2antrr |
|
202 |
|
zre |
|
203 |
|
zre |
|
204 |
|
lenlt |
|
205 |
202 203 204
|
syl2an |
|
206 |
|
zleltp1 |
|
207 |
205 206
|
bitr3d |
|
208 |
199 190 207
|
syl2an |
|
209 |
208
|
biimpa |
|
210 |
201 209
|
gtned |
|
211 |
|
eldifsn |
|
212 |
198 210 211
|
sylanbrc |
|
213 |
197 212
|
ifclda |
|
214 |
|
nfcsb1v |
|
215 |
214
|
nfeq2 |
|
216 |
|
csbeq1a |
|
217 |
216
|
eqeq2d |
|
218 |
215 217
|
rspce |
|
219 |
218
|
ex |
|
220 |
213 219
|
syl |
|
221 |
220
|
rexlimdva |
|
222 |
|
nfv |
|
223 |
|
nfcv |
|
224 |
223 215
|
nfrex |
|
225 |
|
eldifi |
|
226 |
225 60
|
syl |
|
227 |
226
|
nn0ge0d |
|
228 |
227
|
ad2antlr |
|
229 |
226
|
nn0red |
|
230 |
229
|
ad2antlr |
|
231 |
200
|
ad2antrr |
|
232 |
21
|
zred |
|
233 |
232
|
ad2antrr |
|
234 |
|
simpr |
|
235 |
|
elfzle2 |
|
236 |
6 235
|
syl |
|
237 |
236
|
ad2antrr |
|
238 |
230 231 233 234 237
|
ltletrd |
|
239 |
225
|
elfzelzd |
|
240 |
|
zltlem1 |
|
241 |
239 21 240
|
syl2anr |
|
242 |
241
|
adantr |
|
243 |
238 242
|
mpbid |
|
244 |
|
0z |
|
245 |
|
elfz |
|
246 |
244 245
|
mp3an2 |
|
247 |
239 23 246
|
syl2anr |
|
248 |
247
|
adantr |
|
249 |
228 243 248
|
mpbir2and |
|
250 |
|
0red |
|
251 |
200
|
ad2antrr |
|
252 |
229
|
ad2antlr |
|
253 |
|
elfzle1 |
|
254 |
6 253
|
syl |
|
255 |
254
|
ad2antrr |
|
256 |
|
lenlt |
|
257 |
200 229 256
|
syl2an |
|
258 |
257
|
biimpar |
|
259 |
|
eldifsni |
|
260 |
259
|
ad2antlr |
|
261 |
|
ltlen |
|
262 |
200 229 261
|
syl2an |
|
263 |
262
|
adantr |
|
264 |
258 260 263
|
mpbir2and |
|
265 |
250 251 252 255 264
|
lelttrd |
|
266 |
|
zgt0ge1 |
|
267 |
239 266
|
syl |
|
268 |
267
|
ad2antlr |
|
269 |
265 268
|
mpbid |
|
270 |
|
elfzle2 |
|
271 |
225 270
|
syl |
|
272 |
271
|
ad2antlr |
|
273 |
|
1z |
|
274 |
|
elfz |
|
275 |
273 274
|
mp3an2 |
|
276 |
239 21 275
|
syl2anr |
|
277 |
276
|
adantr |
|
278 |
269 272 277
|
mpbir2and |
|
279 |
|
elfzmlbm |
|
280 |
278 279
|
syl |
|
281 |
249 280
|
ifclda |
|
282 |
|
breq1 |
|
283 |
|
id |
|
284 |
|
oveq1 |
|
285 |
282 283 284
|
ifbieq12d |
|
286 |
285
|
eqeq2d |
|
287 |
|
breq1 |
|
288 |
|
id |
|
289 |
|
oveq1 |
|
290 |
287 288 289
|
ifbieq12d |
|
291 |
290
|
eqeq2d |
|
292 |
|
iftrue |
|
293 |
292
|
eqcomd |
|
294 |
293
|
adantl |
|
295 |
|
zlem1lt |
|
296 |
239 199 295
|
syl2anr |
|
297 |
259
|
necomd |
|
298 |
297
|
adantl |
|
299 |
|
ltlen |
|
300 |
229 200 299
|
syl2anr |
|
301 |
300
|
biimprd |
|
302 |
298 301
|
mpan2d |
|
303 |
296 302
|
sylbird |
|
304 |
303
|
con3dimp |
|
305 |
304
|
iffalsed |
|
306 |
226
|
nn0cnd |
|
307 |
|
npcan1 |
|
308 |
306 307
|
syl |
|
309 |
308
|
ad2antlr |
|
310 |
305 309
|
eqtr2d |
|
311 |
286 291 294 310
|
ifbothda |
|
312 |
|
csbeq1a |
|
313 |
311 312
|
syl |
|
314 |
313
|
eqeq2d |
|
315 |
314
|
biimpd |
|
316 |
|
breq1 |
|
317 |
|
id |
|
318 |
|
oveq1 |
|
319 |
316 317 318
|
ifbieq12d |
|
320 |
319
|
csbeq1d |
|
321 |
320
|
eqeq2d |
|
322 |
321
|
rspcev |
|
323 |
281 315 322
|
syl6an |
|
324 |
323
|
ex |
|
325 |
222 224 324
|
rexlimd |
|
326 |
221 325
|
impbid |
|
327 |
187 326
|
bitr3d |
|
328 |
327
|
ralbidv |
|
329 |
132 328
|
syl5bb |
|
330 |
329
|
anbi1d |
|
331 |
1 4 5 6
|
poimirlem23 |
|
332 |
331
|
anbi2d |
|
333 |
131 330 332
|
3bitrd |
|