Step |
Hyp |
Ref |
Expression |
1 |
|
breq2 |
|
2 |
|
breq2 |
|
3 |
2
|
bibi2d |
|
4 |
3
|
notbid |
|
5 |
4
|
2rexbidv |
|
6 |
1 5
|
imbi12d |
|
7 |
6
|
ralbidv |
|
8 |
|
breq2 |
|
9 |
|
breq2 |
|
10 |
9
|
bibi2d |
|
11 |
10
|
notbid |
|
12 |
11
|
2rexbidv |
|
13 |
8 12
|
imbi12d |
|
14 |
13
|
ralbidv |
|
15 |
|
breq2 |
|
16 |
|
breq2 |
|
17 |
16
|
bibi2d |
|
18 |
17
|
notbid |
|
19 |
18
|
2rexbidv |
|
20 |
15 19
|
imbi12d |
|
21 |
20
|
ralbidv |
|
22 |
|
nnnlt1 |
|
23 |
22
|
pm2.21d |
|
24 |
23
|
rgen |
|
25 |
|
exprmfct |
|
26 |
|
prmz |
|
27 |
26
|
adantr |
|
28 |
|
prmnn |
|
29 |
28
|
nnne0d |
|
30 |
29
|
adantr |
|
31 |
|
nnz |
|
32 |
31
|
adantl |
|
33 |
|
dvdsval2 |
|
34 |
27 30 32 33
|
syl3anc |
|
35 |
34
|
biimpd |
|
36 |
35
|
3ad2antl2 |
|
37 |
36
|
adantrl |
|
38 |
|
simprr |
|
39 |
|
nnre |
|
40 |
|
nngt0 |
|
41 |
39 40
|
jca |
|
42 |
|
nnre |
|
43 |
|
nngt0 |
|
44 |
42 43
|
jca |
|
45 |
28 44
|
syl |
|
46 |
|
divgt0 |
|
47 |
41 45 46
|
syl2anr |
|
48 |
47
|
3ad2antl2 |
|
49 |
48
|
adantrr |
|
50 |
|
elnnz |
|
51 |
38 49 50
|
sylanbrc |
|
52 |
51
|
expr |
|
53 |
52
|
adantrl |
|
54 |
26
|
adantr |
|
55 |
29
|
adantr |
|
56 |
|
eluzelz |
|
57 |
56
|
adantl |
|
58 |
|
dvdsval2 |
|
59 |
54 55 57 58
|
syl3anc |
|
60 |
|
eluzelre |
|
61 |
|
2z |
|
62 |
61
|
eluz1i |
|
63 |
|
2pos |
|
64 |
|
zre |
|
65 |
|
0re |
|
66 |
|
2re |
|
67 |
|
ltletr |
|
68 |
65 66 67
|
mp3an12 |
|
69 |
64 68
|
syl |
|
70 |
63 69
|
mpani |
|
71 |
70
|
imp |
|
72 |
62 71
|
sylbi |
|
73 |
60 72
|
jca |
|
74 |
|
divgt0 |
|
75 |
73 45 74
|
syl2anr |
|
76 |
75
|
a1d |
|
77 |
76
|
ancld |
|
78 |
|
elnnz |
|
79 |
77 78
|
syl6ibr |
|
80 |
59 79
|
sylbid |
|
81 |
80
|
ancoms |
|
82 |
|
breq1 |
|
83 |
|
breq2 |
|
84 |
|
breq2 |
|
85 |
84
|
bibi2d |
|
86 |
85
|
notbid |
|
87 |
86
|
2rexbidv |
|
88 |
83 87
|
imbi12d |
|
89 |
88
|
ralbidv |
|
90 |
82 89
|
imbi12d |
|
91 |
90
|
rspcv |
|
92 |
91
|
3ad2ant1 |
|
93 |
92
|
adantl |
|
94 |
|
eluzelcn |
|
95 |
94
|
mulid2d |
|
96 |
95
|
ad2antrr |
|
97 |
|
prmgt1 |
|
98 |
97
|
ad2antlr |
|
99 |
|
1red |
|
100 |
28
|
nnred |
|
101 |
100
|
ad2antlr |
|
102 |
60
|
ad2antrr |
|
103 |
72
|
ad2antrr |
|
104 |
|
ltmul1 |
|
105 |
99 101 102 103 104
|
syl112anc |
|
106 |
98 105
|
mpbid |
|
107 |
96 106
|
eqbrtrrd |
|
108 |
28 43
|
syl |
|
109 |
108
|
ad2antlr |
|
110 |
|
ltdivmul |
|
111 |
102 102 101 109 110
|
syl112anc |
|
112 |
107 111
|
mpbird |
|
113 |
|
breq1 |
|
114 |
|
breq2 |
|
115 |
114
|
bibi1d |
|
116 |
115
|
notbid |
|
117 |
116
|
2rexbidv |
|
118 |
113 117
|
imbi12d |
|
119 |
118
|
rspcv |
|
120 |
119
|
3ad2ant2 |
|
121 |
120
|
adantl |
|
122 |
39
|
3ad2ant3 |
|
123 |
122
|
adantl |
|
124 |
|
ltdiv1 |
|
125 |
123 102 101 109 124
|
syl112anc |
|
126 |
125
|
biimpa |
|
127 |
|
simprll |
|
128 |
|
peano2nn |
|
129 |
128
|
adantl |
|
130 |
129
|
ad2antrl |
|
131 |
26
|
ad4antlr |
|
132 |
|
nnnn0 |
|
133 |
132
|
ad2antll |
|
134 |
|
zexpcl |
|
135 |
131 133 134
|
syl2anc |
|
136 |
|
nnz |
|
137 |
136
|
3ad2ant2 |
|
138 |
137
|
ad3antlr |
|
139 |
29
|
ad4antlr |
|
140 |
|
dvdsmulcr |
|
141 |
135 138 131 139 140
|
syl112anc |
|
142 |
28
|
nncnd |
|
143 |
142
|
ad4antlr |
|
144 |
143 133
|
expp1d |
|
145 |
144
|
eqcomd |
|
146 |
|
nncn |
|
147 |
146
|
3ad2ant3 |
|
148 |
147
|
ad3antlr |
|
149 |
148 143 139
|
divcan1d |
|
150 |
145 149
|
breq12d |
|
151 |
141 150
|
bitr3d |
|
152 |
|
nnz |
|
153 |
152
|
3ad2ant1 |
|
154 |
153
|
ad3antlr |
|
155 |
|
dvdsmulcr |
|
156 |
135 154 131 139 155
|
syl112anc |
|
157 |
94
|
ad4antr |
|
158 |
157 143 139
|
divcan1d |
|
159 |
145 158
|
breq12d |
|
160 |
156 159
|
bitr3d |
|
161 |
151 160
|
bibi12d |
|
162 |
161
|
notbid |
|
163 |
162
|
biimpd |
|
164 |
163
|
impr |
|
165 |
|
oveq2 |
|
166 |
165
|
breq1d |
|
167 |
165
|
breq1d |
|
168 |
166 167
|
bibi12d |
|
169 |
168
|
notbid |
|
170 |
169
|
rspcev |
|
171 |
130 164 170
|
syl2anc |
|
172 |
|
oveq1 |
|
173 |
172
|
breq1d |
|
174 |
172
|
breq1d |
|
175 |
173 174
|
bibi12d |
|
176 |
175
|
notbid |
|
177 |
176
|
anbi2d |
|
178 |
177
|
anbi2d |
|
179 |
|
oveq1 |
|
180 |
179
|
breq1d |
|
181 |
179
|
breq1d |
|
182 |
180 181
|
bibi12d |
|
183 |
182
|
notbid |
|
184 |
183
|
rexbidv |
|
185 |
178 184
|
imbi12d |
|
186 |
171 185
|
mpbiri |
|
187 |
186
|
com12 |
|
188 |
|
simplr |
|
189 |
188
|
ad2antlr |
|
190 |
|
prmz |
|
191 |
190
|
adantr |
|
192 |
191
|
ad2antrl |
|
193 |
132
|
adantl |
|
194 |
193
|
ad2antrl |
|
195 |
|
zexpcl |
|
196 |
192 194 195
|
syl2anc |
|
197 |
26
|
ad4antlr |
|
198 |
137
|
ad3antlr |
|
199 |
|
dvdsmultr2 |
|
200 |
196 197 198 199
|
syl3anc |
|
201 |
196 197
|
gcdcomd |
|
202 |
|
simp-4r |
|
203 |
|
simprl |
|
204 |
|
simprr |
|
205 |
|
prmdvdsexpb |
|
206 |
|
equcom |
|
207 |
205 206
|
syl6bb |
|
208 |
207
|
biimpd |
|
209 |
202 203 204 208
|
syl3anc |
|
210 |
209
|
con3d |
|
211 |
210
|
impr |
|
212 |
|
simp-4r |
|
213 |
|
coprm |
|
214 |
212 196 213
|
syl2anc |
|
215 |
211 214
|
mpbid |
|
216 |
201 215
|
eqtrd |
|
217 |
|
coprmdvds |
|
218 |
196 197 198 217
|
syl3anc |
|
219 |
216 218
|
mpan2d |
|
220 |
200 219
|
impbid |
|
221 |
147
|
ad3antlr |
|
222 |
142
|
ad4antlr |
|
223 |
29
|
ad4antlr |
|
224 |
221 222 223
|
divcan2d |
|
225 |
224
|
breq2d |
|
226 |
220 225
|
bitrd |
|
227 |
153
|
ad3antlr |
|
228 |
|
dvdsmultr2 |
|
229 |
196 197 227 228
|
syl3anc |
|
230 |
|
coprmdvds |
|
231 |
196 197 227 230
|
syl3anc |
|
232 |
216 231
|
mpan2d |
|
233 |
229 232
|
impbid |
|
234 |
94
|
ad4antr |
|
235 |
234 222 223
|
divcan2d |
|
236 |
235
|
breq2d |
|
237 |
233 236
|
bitrd |
|
238 |
226 237
|
bibi12d |
|
239 |
238
|
notbid |
|
240 |
239
|
biimpa |
|
241 |
|
oveq2 |
|
242 |
241
|
breq1d |
|
243 |
241
|
breq1d |
|
244 |
242 243
|
bibi12d |
|
245 |
244
|
notbid |
|
246 |
245
|
rspcev |
|
247 |
189 240 246
|
syl2anc |
|
248 |
247
|
ex |
|
249 |
248
|
expr |
|
250 |
249
|
com23 |
|
251 |
250
|
impr |
|
252 |
187 251
|
pm2.61d |
|
253 |
|
oveq1 |
|
254 |
253
|
breq1d |
|
255 |
253
|
breq1d |
|
256 |
254 255
|
bibi12d |
|
257 |
256
|
notbid |
|
258 |
257
|
rexbidv |
|
259 |
258
|
rspcev |
|
260 |
127 252 259
|
syl2anc |
|
261 |
260
|
exp32 |
|
262 |
261
|
rexlimdvv |
|
263 |
126 262
|
embantd |
|
264 |
263
|
ex |
|
265 |
264
|
com23 |
|
266 |
121 265
|
syld |
|
267 |
112 266
|
embantd |
|
268 |
93 267
|
syld |
|
269 |
268
|
3exp2 |
|
270 |
81 269
|
syld |
|
271 |
270
|
3impia |
|
272 |
271
|
com24 |
|
273 |
272
|
imp32 |
|
274 |
37 53 273
|
3syld |
|
275 |
|
simpl2 |
|
276 |
|
1nn |
|
277 |
276
|
a1i |
|
278 |
142
|
exp1d |
|
279 |
278
|
breq1d |
|
280 |
279
|
notbid |
|
281 |
280
|
biimpar |
|
282 |
281
|
3ad2antl2 |
|
283 |
282
|
adantrr |
|
284 |
283
|
adantrl |
|
285 |
278
|
breq1d |
|
286 |
285
|
biimpar |
|
287 |
286
|
3adant1 |
|
288 |
|
idd |
|
289 |
287 288
|
mpid |
|
290 |
289
|
adantr |
|
291 |
284 290
|
mtod |
|
292 |
|
biimpr |
|
293 |
291 292
|
nsyl |
|
294 |
|
oveq1 |
|
295 |
294
|
breq1d |
|
296 |
294
|
breq1d |
|
297 |
295 296
|
bibi12d |
|
298 |
297
|
notbid |
|
299 |
|
oveq2 |
|
300 |
299
|
breq1d |
|
301 |
299
|
breq1d |
|
302 |
300 301
|
bibi12d |
|
303 |
302
|
notbid |
|
304 |
298 303
|
rspc2ev |
|
305 |
275 277 293 304
|
syl3anc |
|
306 |
305
|
expr |
|
307 |
306
|
expd |
|
308 |
307
|
adantrl |
|
309 |
274 308
|
pm2.61d |
|
310 |
309
|
expr |
|
311 |
310
|
ralrimiv |
|
312 |
|
breq1 |
|
313 |
|
breq2 |
|
314 |
313
|
bibi1d |
|
315 |
314
|
notbid |
|
316 |
315
|
2rexbidv |
|
317 |
253
|
breq1d |
|
318 |
317 255
|
bibi12d |
|
319 |
318
|
notbid |
|
320 |
241
|
breq1d |
|
321 |
320 243
|
bibi12d |
|
322 |
321
|
notbid |
|
323 |
319 322
|
cbvrex2vw |
|
324 |
316 323
|
syl6bb |
|
325 |
312 324
|
imbi12d |
|
326 |
325
|
cbvralvw |
|
327 |
311 326
|
sylib |
|
328 |
327
|
3exp1 |
|
329 |
328
|
rexlimdv |
|
330 |
25 329
|
mpd |
|
331 |
14 21 24 330
|
indstr2 |
|
332 |
7 331
|
vtoclga |
|