Step |
Hyp |
Ref |
Expression |
1 |
|
iblspltprt.1 |
|
2 |
|
iblspltprt.2 |
|
3 |
|
iblspltprt.3 |
|
4 |
|
iblspltprt.4 |
|
5 |
|
iblspltprt.5 |
|
6 |
|
iblspltprt.6 |
|
7 |
|
iblspltprt.7 |
|
8 |
|
eluzelz |
|
9 |
3 8
|
syl |
|
10 |
|
eluzle |
|
11 |
3 10
|
syl |
|
12 |
9
|
zred |
|
13 |
12
|
leidd |
|
14 |
2
|
peano2zd |
|
15 |
|
elfz1 |
|
16 |
14 9 15
|
syl2anc |
|
17 |
9 11 13 16
|
mpbir3and |
|
18 |
|
fveq2 |
|
19 |
18
|
oveq2d |
|
20 |
19
|
mpteq1d |
|
21 |
20
|
eleq1d |
|
22 |
21
|
imbi2d |
|
23 |
|
fveq2 |
|
24 |
23
|
oveq2d |
|
25 |
24
|
mpteq1d |
|
26 |
25
|
eleq1d |
|
27 |
26
|
imbi2d |
|
28 |
|
fveq2 |
|
29 |
28
|
oveq2d |
|
30 |
29
|
mpteq1d |
|
31 |
30
|
eleq1d |
|
32 |
31
|
imbi2d |
|
33 |
|
fveq2 |
|
34 |
33
|
oveq2d |
|
35 |
34
|
mpteq1d |
|
36 |
35
|
eleq1d |
|
37 |
36
|
imbi2d |
|
38 |
|
uzid |
|
39 |
2 38
|
syl |
|
40 |
2
|
zred |
|
41 |
|
1red |
|
42 |
40 41
|
readdcld |
|
43 |
40
|
ltp1d |
|
44 |
40 42 12 43 11
|
ltletrd |
|
45 |
|
elfzo2 |
|
46 |
39 9 44 45
|
syl3anbrc |
|
47 |
|
fveq2 |
|
48 |
|
fvoveq1 |
|
49 |
47 48
|
oveq12d |
|
50 |
49
|
mpteq1d |
|
51 |
50
|
eleq1d |
|
52 |
51
|
imbi2d |
|
53 |
7
|
expcom |
|
54 |
52 53
|
vtoclga |
|
55 |
46 54
|
mpcom |
|
56 |
55
|
a1i |
|
57 |
|
nfv |
|
58 |
|
nfmpt1 |
|
59 |
58
|
nfel1 |
|
60 |
1 59
|
nfim |
|
61 |
57 60 1
|
nf3an |
|
62 |
|
simp3 |
|
63 |
|
simp1 |
|
64 |
40
|
leidd |
|
65 |
40 12 44
|
ltled |
|
66 |
|
elfz1 |
|
67 |
2 9 66
|
syl2anc |
|
68 |
2 64 65 67
|
mpbir3and |
|
69 |
68
|
ancli |
|
70 |
|
eleq1 |
|
71 |
70
|
anbi2d |
|
72 |
47
|
eleq1d |
|
73 |
71 72
|
imbi12d |
|
74 |
73 4
|
vtoclg |
|
75 |
68 69 74
|
sylc |
|
76 |
75
|
adantr |
|
77 |
76
|
rexrd |
|
78 |
|
simpl |
|
79 |
|
elfzoelz |
|
80 |
79
|
adantl |
|
81 |
40
|
adantr |
|
82 |
80
|
zred |
|
83 |
42
|
adantr |
|
84 |
43
|
adantr |
|
85 |
|
elfzole1 |
|
86 |
85
|
adantl |
|
87 |
81 83 82 84 86
|
ltletrd |
|
88 |
81 82 87
|
ltled |
|
89 |
12
|
adantr |
|
90 |
|
elfzolt2 |
|
91 |
90
|
adantl |
|
92 |
82 89 91
|
ltled |
|
93 |
2 9
|
jca |
|
94 |
93
|
adantr |
|
95 |
|
elfz1 |
|
96 |
94 95
|
syl |
|
97 |
80 88 92 96
|
mpbir3and |
|
98 |
|
eleq1 |
|
99 |
98
|
anbi2d |
|
100 |
|
fveq2 |
|
101 |
100
|
eleq1d |
|
102 |
99 101
|
imbi12d |
|
103 |
102 4
|
chvarvv |
|
104 |
78 97 103
|
syl2anc |
|
105 |
104
|
rexrd |
|
106 |
80
|
peano2zd |
|
107 |
106
|
zred |
|
108 |
|
1red |
|
109 |
81 82 108 87
|
ltadd1dd |
|
110 |
81 83 107 84 109
|
lttrd |
|
111 |
81 107 110
|
ltled |
|
112 |
|
zltp1le |
|
113 |
79 9 112
|
syl2anr |
|
114 |
91 113
|
mpbid |
|
115 |
|
elfz1 |
|
116 |
94 115
|
syl |
|
117 |
106 111 114 116
|
mpbir3and |
|
118 |
78 117
|
jca |
|
119 |
|
eleq1 |
|
120 |
119
|
anbi2d |
|
121 |
|
fveq2 |
|
122 |
121
|
eleq1d |
|
123 |
120 122
|
imbi12d |
|
124 |
123 4
|
vtoclg |
|
125 |
117 118 124
|
sylc |
|
126 |
125
|
rexrd |
|
127 |
|
eluz |
|
128 |
2 79 127
|
syl2an |
|
129 |
88 128
|
mpbird |
|
130 |
|
simpll |
|
131 |
|
elfzelz |
|
132 |
131
|
adantl |
|
133 |
|
elfzle1 |
|
134 |
133
|
adantl |
|
135 |
132
|
zred |
|
136 |
130 12
|
syl |
|
137 |
82
|
adantr |
|
138 |
|
elfzle2 |
|
139 |
138
|
adantl |
|
140 |
91
|
adantr |
|
141 |
135 137 136 139 140
|
lelttrd |
|
142 |
135 136 141
|
ltled |
|
143 |
|
elfz1 |
|
144 |
130 93 143
|
3syl |
|
145 |
132 134 142 144
|
mpbir3and |
|
146 |
130 145 4
|
syl2anc |
|
147 |
|
simpll |
|
148 |
|
elfzelz |
|
149 |
148
|
adantl |
|
150 |
|
elfzle1 |
|
151 |
150
|
adantl |
|
152 |
149
|
zred |
|
153 |
147 12
|
syl |
|
154 |
82
|
adantr |
|
155 |
|
1red |
|
156 |
154 155
|
resubcld |
|
157 |
|
elfzle2 |
|
158 |
157
|
adantl |
|
159 |
79
|
zred |
|
160 |
|
1red |
|
161 |
159 160
|
resubcld |
|
162 |
|
elfzoel2 |
|
163 |
162
|
zred |
|
164 |
159
|
ltm1d |
|
165 |
161 159 163 164 90
|
lttrd |
|
166 |
165
|
ad2antlr |
|
167 |
152 156 153 158 166
|
lelttrd |
|
168 |
152 153 167
|
ltled |
|
169 |
147 93 143
|
3syl |
|
170 |
149 151 168 169
|
mpbir3and |
|
171 |
147 170 4
|
syl2anc |
|
172 |
149
|
peano2zd |
|
173 |
|
elfzel1 |
|
174 |
173
|
zred |
|
175 |
148
|
zred |
|
176 |
|
1red |
|
177 |
175 176
|
readdcld |
|
178 |
175
|
ltp1d |
|
179 |
174 175 177 150 178
|
lelttrd |
|
180 |
174 177 179
|
ltled |
|
181 |
180
|
adantl |
|
182 |
147 3 8
|
3syl |
|
183 |
|
zltp1le |
|
184 |
149 182 183
|
syl2anc |
|
185 |
167 184
|
mpbid |
|
186 |
|
elfz1 |
|
187 |
147 93 186
|
3syl |
|
188 |
172 181 185 187
|
mpbir3and |
|
189 |
147 188
|
jca |
|
190 |
|
eleq1 |
|
191 |
190
|
anbi2d |
|
192 |
|
fveq2 |
|
193 |
192
|
eleq1d |
|
194 |
191 193
|
imbi12d |
|
195 |
194 103
|
vtoclg |
|
196 |
188 189 195
|
sylc |
|
197 |
|
elfzuz |
|
198 |
197
|
adantl |
|
199 |
|
elfzo2 |
|
200 |
198 182 167 199
|
syl3anbrc |
|
201 |
147 200 5
|
syl2anc |
|
202 |
171 196 201
|
ltled |
|
203 |
129 146 202
|
monoord |
|
204 |
162
|
adantl |
|
205 |
|
elfzo2 |
|
206 |
129 204 91 205
|
syl3anbrc |
|
207 |
|
eleq1 |
|
208 |
207
|
anbi2d |
|
209 |
|
fvoveq1 |
|
210 |
100 209
|
breq12d |
|
211 |
208 210
|
imbi12d |
|
212 |
211 5
|
chvarvv |
|
213 |
78 206 212
|
syl2anc |
|
214 |
104 125 213
|
ltled |
|
215 |
|
iccintsng |
|
216 |
77 105 126 203 214 215
|
syl32anc |
|
217 |
216
|
fveq2d |
|
218 |
|
ovolsn |
|
219 |
104 218
|
syl |
|
220 |
217 219
|
eqtrd |
|
221 |
62 63 220
|
syl2anc |
|
222 |
76 125 104 203 214
|
eliccd |
|
223 |
76 125 222
|
3jca |
|
224 |
62 63 223
|
syl2anc |
|
225 |
|
iccsplit |
|
226 |
224 225
|
syl |
|
227 |
|
simpl3 |
|
228 |
|
simpl1 |
|
229 |
|
simpr |
|
230 |
|
simp1 |
|
231 |
|
eliccxr |
|
232 |
231
|
3ad2ant3 |
|
233 |
75
|
rexrd |
|
234 |
233
|
3ad2ant1 |
|
235 |
126
|
3adant3 |
|
236 |
|
simp3 |
|
237 |
|
iccgelb |
|
238 |
234 235 236 237
|
syl3anc |
|
239 |
76 125
|
jca |
|
240 |
239
|
3adant3 |
|
241 |
|
iccssre |
|
242 |
241
|
sseld |
|
243 |
240 236 242
|
sylc |
|
244 |
125
|
3adant3 |
|
245 |
|
elfz1 |
|
246 |
2 9 245
|
syl2anc |
|
247 |
9 65 13 246
|
mpbir3and |
|
248 |
247
|
ancli |
|
249 |
|
eleq1 |
|
250 |
249
|
anbi2d |
|
251 |
|
fveq2 |
|
252 |
251
|
eleq1d |
|
253 |
250 252
|
imbi12d |
|
254 |
253 4
|
vtoclg |
|
255 |
9 248 254
|
sylc |
|
256 |
255
|
3ad2ant1 |
|
257 |
|
elicc1 |
|
258 |
234 235 257
|
syl2anc |
|
259 |
236 258
|
mpbid |
|
260 |
259
|
simp3d |
|
261 |
|
elfzop1le2 |
|
262 |
79
|
peano2zd |
|
263 |
|
eluz |
|
264 |
262 162 263
|
syl2anc |
|
265 |
261 264
|
mpbird |
|
266 |
265
|
adantl |
|
267 |
|
simpll |
|
268 |
|
elfzelz |
|
269 |
268
|
adantl |
|
270 |
267 40
|
syl |
|
271 |
269
|
zred |
|
272 |
82
|
adantr |
|
273 |
87
|
adantr |
|
274 |
159
|
adantr |
|
275 |
|
1red |
|
276 |
274 275
|
readdcld |
|
277 |
268
|
zred |
|
278 |
277
|
adantl |
|
279 |
274
|
ltp1d |
|
280 |
|
elfzle1 |
|
281 |
280
|
adantl |
|
282 |
274 276 278 279 281
|
ltletrd |
|
283 |
282
|
adantll |
|
284 |
270 272 271 273 283
|
lttrd |
|
285 |
270 271 284
|
ltled |
|
286 |
|
elfzle2 |
|
287 |
286
|
adantl |
|
288 |
267 93 143
|
3syl |
|
289 |
269 285 287 288
|
mpbir3and |
|
290 |
267 289 4
|
syl2anc |
|
291 |
|
simpll |
|
292 |
|
elfzelz |
|
293 |
292
|
adantl |
|
294 |
291 40
|
syl |
|
295 |
293
|
zred |
|
296 |
82
|
adantr |
|
297 |
87
|
adantr |
|
298 |
159
|
adantr |
|
299 |
|
1red |
|
300 |
298 299
|
readdcld |
|
301 |
292
|
zred |
|
302 |
301
|
adantl |
|
303 |
298
|
ltp1d |
|
304 |
|
elfzle1 |
|
305 |
304
|
adantl |
|
306 |
298 300 302 303 305
|
ltletrd |
|
307 |
306
|
adantll |
|
308 |
294 296 295 297 307
|
lttrd |
|
309 |
294 295 308
|
ltled |
|
310 |
301
|
adantl |
|
311 |
12
|
adantr |
|
312 |
|
1red |
|
313 |
311 312
|
resubcld |
|
314 |
|
elfzle2 |
|
315 |
314
|
adantl |
|
316 |
311
|
ltm1d |
|
317 |
310 313 311 315 316
|
lelttrd |
|
318 |
310 311 317
|
ltled |
|
319 |
318
|
adantlr |
|
320 |
291 93 143
|
3syl |
|
321 |
293 309 319 320
|
mpbir3and |
|
322 |
291 321 4
|
syl2anc |
|
323 |
293
|
peano2zd |
|
324 |
323
|
zred |
|
325 |
302 299
|
readdcld |
|
326 |
298 302 306
|
ltled |
|
327 |
298 302 299 326
|
leadd1dd |
|
328 |
298 300 325 303 327
|
ltletrd |
|
329 |
328
|
adantll |
|
330 |
294 296 324 297 329
|
lttrd |
|
331 |
294 324 330
|
ltled |
|
332 |
292 9 183
|
syl2anr |
|
333 |
317 332
|
mpbid |
|
334 |
333
|
adantlr |
|
335 |
291 93 186
|
3syl |
|
336 |
323 331 334 335
|
mpbir3and |
|
337 |
291 336
|
jca |
|
338 |
336 337 195
|
sylc |
|
339 |
291 2
|
syl |
|
340 |
|
eluz |
|
341 |
339 293 340
|
syl2anc |
|
342 |
309 341
|
mpbird |
|
343 |
291 3 8
|
3syl |
|
344 |
317
|
adantlr |
|
345 |
342 343 344 199
|
syl3anbrc |
|
346 |
291 345 5
|
syl2anc |
|
347 |
322 338 346
|
ltled |
|
348 |
266 290 347
|
monoord |
|
349 |
348
|
3adant3 |
|
350 |
243 244 256 260 349
|
letrd |
|
351 |
256
|
rexrd |
|
352 |
|
elicc1 |
|
353 |
234 351 352
|
syl2anc |
|
354 |
232 238 350 353
|
mpbir3and |
|
355 |
230 354 6
|
syl2anc |
|
356 |
227 228 229 355
|
syl3anc |
|
357 |
|
simp2 |
|
358 |
62 357
|
mpd |
|
359 |
62 63
|
jca |
|
360 |
78 206
|
jca |
|
361 |
100 209
|
oveq12d |
|
362 |
361
|
mpteq1d |
|
363 |
362
|
eleq1d |
|
364 |
208 363
|
imbi12d |
|
365 |
364 7
|
chvarvv |
|
366 |
359 360 365
|
3syl |
|
367 |
61 221 226 356 358 366
|
iblsplitf |
|
368 |
367
|
3exp |
|
369 |
22 27 32 37 56 368
|
fzind2 |
|
370 |
17 369
|
mpcom |
|