Step |
Hyp |
Ref |
Expression |
1 |
|
efrlim.1 |
|
2 |
|
rge0ssre |
|
3 |
|
ax-resscn |
|
4 |
2 3
|
sstri |
|
5 |
4
|
sseli |
|
6 |
|
simpll |
|
7 |
|
1cnd |
|
8 |
|
simplr |
|
9 |
|
ax-1ne0 |
|
10 |
9
|
a1i |
|
11 |
|
simpr |
|
12 |
11
|
neqned |
|
13 |
6 7 8 10 12
|
divdiv2d |
|
14 |
|
mulcl |
|
15 |
14
|
adantr |
|
16 |
15
|
div1d |
|
17 |
13 16
|
eqtrd |
|
18 |
17
|
oveq2d |
|
19 |
18
|
oveq1d |
|
20 |
19
|
ifeq2da |
|
21 |
5 20
|
sylan2 |
|
22 |
21
|
mpteq2dva |
|
23 |
|
resmpt |
|
24 |
4 23
|
ax-mp |
|
25 |
22 24
|
eqtr4di |
|
26 |
|
0e0icopnf |
|
27 |
26
|
a1i |
|
28 |
|
eqeq2 |
|
29 |
|
eqeq2 |
|
30 |
|
cnxmet |
|
31 |
|
0cnd |
|
32 |
|
abscl |
|
33 |
|
peano2re |
|
34 |
32 33
|
syl |
|
35 |
|
0red |
|
36 |
|
absge0 |
|
37 |
32
|
ltp1d |
|
38 |
35 32 34 36 37
|
lelttrd |
|
39 |
34 38
|
elrpd |
|
40 |
39
|
rpreccld |
|
41 |
40
|
rpxrd |
|
42 |
|
blssm |
|
43 |
30 31 41 42
|
mp3an2i |
|
44 |
1 43
|
eqsstrid |
|
45 |
44
|
sselda |
|
46 |
|
mul0or |
|
47 |
45 46
|
syldan |
|
48 |
47
|
biimpa |
|
49 |
8 12
|
reccld |
|
50 |
45 49
|
syldanl |
|
51 |
50
|
adantlr |
|
52 |
51
|
1cxpd |
|
53 |
|
simplr |
|
54 |
53
|
oveq1d |
|
55 |
45
|
ad2antrr |
|
56 |
55
|
mul02d |
|
57 |
54 56
|
eqtrd |
|
58 |
57
|
oveq2d |
|
59 |
|
1p0e1 |
|
60 |
58 59
|
eqtrdi |
|
61 |
60
|
oveq1d |
|
62 |
53
|
fveq2d |
|
63 |
|
ef0 |
|
64 |
62 63
|
eqtrdi |
|
65 |
52 61 64
|
3eqtr4d |
|
66 |
65
|
ifeq2da |
|
67 |
|
ifid |
|
68 |
66 67
|
eqtrdi |
|
69 |
|
iftrue |
|
70 |
69
|
adantl |
|
71 |
68 70
|
jaodan |
|
72 |
|
mulid1 |
|
73 |
72
|
ad2antrr |
|
74 |
73
|
fveq2d |
|
75 |
71 74
|
eqtr4d |
|
76 |
48 75
|
syldan |
|
77 |
|
mulne0b |
|
78 |
45 77
|
syldan |
|
79 |
|
df-ne |
|
80 |
78 79
|
bitrdi |
|
81 |
|
simprr |
|
82 |
81
|
neneqd |
|
83 |
82
|
iffalsed |
|
84 |
|
ax-1cn |
|
85 |
45 14
|
syldan |
|
86 |
|
addcl |
|
87 |
84 85 86
|
sylancr |
|
88 |
87
|
adantr |
|
89 |
|
eqid |
|
90 |
89
|
dvlog2lem |
|
91 |
|
eqid |
|
92 |
91
|
logdmss |
|
93 |
90 92
|
sstri |
|
94 |
|
eqid |
|
95 |
94
|
cnmetdval |
|
96 |
87 84 95
|
sylancl |
|
97 |
|
pncan2 |
|
98 |
84 85 97
|
sylancr |
|
99 |
98
|
fveq2d |
|
100 |
96 99
|
eqtrd |
|
101 |
85
|
abscld |
|
102 |
34
|
adantr |
|
103 |
45
|
abscld |
|
104 |
102 103
|
remulcld |
|
105 |
|
1red |
|
106 |
|
absmul |
|
107 |
45 106
|
syldan |
|
108 |
32
|
adantr |
|
109 |
108 33
|
syl |
|
110 |
45
|
absge0d |
|
111 |
108
|
lep1d |
|
112 |
108 109 103 110 111
|
lemul1ad |
|
113 |
107 112
|
eqbrtrd |
|
114 |
|
0cn |
|
115 |
94
|
cnmetdval |
|
116 |
45 114 115
|
sylancl |
|
117 |
45
|
subid1d |
|
118 |
117
|
fveq2d |
|
119 |
116 118
|
eqtrd |
|
120 |
|
simpr |
|
121 |
120 1
|
eleqtrdi |
|
122 |
30
|
a1i |
|
123 |
41
|
adantr |
|
124 |
|
0cnd |
|
125 |
|
elbl3 |
|
126 |
122 123 124 45 125
|
syl22anc |
|
127 |
121 126
|
mpbid |
|
128 |
119 127
|
eqbrtrrd |
|
129 |
38
|
adantr |
|
130 |
|
ltmuldiv2 |
|
131 |
103 105 109 129 130
|
syl112anc |
|
132 |
128 131
|
mpbird |
|
133 |
101 104 105 113 132
|
lelttrd |
|
134 |
100 133
|
eqbrtrd |
|
135 |
|
1rp |
|
136 |
|
rpxr |
|
137 |
135 136
|
mp1i |
|
138 |
|
1cnd |
|
139 |
|
elbl3 |
|
140 |
122 137 138 87 139
|
syl22anc |
|
141 |
134 140
|
mpbird |
|
142 |
93 141
|
sselid |
|
143 |
|
eldifsni |
|
144 |
142 143
|
syl |
|
145 |
144
|
adantr |
|
146 |
45
|
adantr |
|
147 |
146 81
|
reccld |
|
148 |
88 145 147
|
cxpefd |
|
149 |
87 144
|
logcld |
|
150 |
149
|
adantr |
|
151 |
147 150
|
mulcomd |
|
152 |
|
simpll |
|
153 |
|
simprl |
|
154 |
152 153
|
dividd |
|
155 |
154
|
oveq1d |
|
156 |
152 152 146 153 81
|
divdiv1d |
|
157 |
155 156
|
eqtr3d |
|
158 |
157
|
oveq2d |
|
159 |
85
|
adantr |
|
160 |
78
|
biimpa |
|
161 |
150 152 159 160
|
div12d |
|
162 |
151 158 161
|
3eqtrd |
|
163 |
162
|
fveq2d |
|
164 |
83 148 163
|
3eqtrd |
|
165 |
164
|
ex |
|
166 |
80 165
|
sylbird |
|
167 |
166
|
imp |
|
168 |
28 29 76 167
|
ifbothda |
|
169 |
168
|
mpteq2dva |
|
170 |
44
|
resmptd |
|
171 |
|
1cnd |
|
172 |
149
|
adantr |
|
173 |
85
|
adantr |
|
174 |
|
simpr |
|
175 |
174
|
neqned |
|
176 |
172 173 175
|
divcld |
|
177 |
171 176
|
ifclda |
|
178 |
|
eqidd |
|
179 |
|
eqidd |
|
180 |
|
oveq2 |
|
181 |
180
|
fveq2d |
|
182 |
|
oveq2 |
|
183 |
182
|
fveq2d |
|
184 |
|
oveq2 |
|
185 |
184
|
fveq2d |
|
186 |
183 185
|
ifsb |
|
187 |
181 186
|
eqtrdi |
|
188 |
177 178 179 187
|
fmptco |
|
189 |
169 170 188
|
3eqtr4d |
|
190 |
|
eqidd |
|
191 |
|
eqidd |
|
192 |
|
eqeq1 |
|
193 |
|
fveq2 |
|
194 |
|
oveq1 |
|
195 |
193 194
|
oveq12d |
|
196 |
192 195
|
ifbieq2d |
|
197 |
141 190 191 196
|
fmptco |
|
198 |
59
|
eqeq2i |
|
199 |
138 85 124
|
addcand |
|
200 |
198 199
|
bitr3id |
|
201 |
98
|
oveq2d |
|
202 |
200 201
|
ifbieq2d |
|
203 |
202
|
mpteq2dva |
|
204 |
197 203
|
eqtrd |
|
205 |
|
eqid |
|
206 |
|
eqid |
|
207 |
206
|
cnfldtopon |
|
208 |
207
|
a1i |
|
209 |
|
1cnd |
|
210 |
208 208 209
|
cnmptc |
|
211 |
|
id |
|
212 |
208 208 211
|
cnmptc |
|
213 |
208
|
cnmptid |
|
214 |
206
|
mulcn |
|
215 |
214
|
a1i |
|
216 |
208 212 213 215
|
cnmpt12f |
|
217 |
206
|
addcn |
|
218 |
217
|
a1i |
|
219 |
208 210 216 218
|
cnmpt12f |
|
220 |
205 208 44 219
|
cnmpt1res |
|
221 |
141
|
fmpttd |
|
222 |
221
|
frnd |
|
223 |
|
difss |
|
224 |
93 223
|
sstri |
|
225 |
224
|
a1i |
|
226 |
|
cnrest2 |
|
227 |
207 222 225 226
|
mp3an2i |
|
228 |
220 227
|
mpbid |
|
229 |
|
blcntr |
|
230 |
30 31 40 229
|
mp3an2i |
|
231 |
230 1
|
eleqtrrdi |
|
232 |
|
resttopon |
|
233 |
207 44 232
|
sylancr |
|
234 |
|
toponuni |
|
235 |
233 234
|
syl |
|
236 |
231 235
|
eleqtrd |
|
237 |
|
eqid |
|
238 |
237
|
cncnpi |
|
239 |
228 236 238
|
syl2anc |
|
240 |
|
cnelprrecn |
|
241 |
|
logf1o |
|
242 |
|
f1of |
|
243 |
241 242
|
ax-mp |
|
244 |
|
logrncn |
|
245 |
244
|
ssriv |
|
246 |
|
fss |
|
247 |
243 245 246
|
mp2an |
|
248 |
|
fssres |
|
249 |
247 93 248
|
mp2an |
|
250 |
|
blcntr |
|
251 |
30 84 135 250
|
mp3an |
|
252 |
|
ovex |
|
253 |
89
|
dvlog2 |
|
254 |
252 253
|
dmmpti |
|
255 |
251 254
|
eleqtrri |
|
256 |
|
eqid |
|
257 |
253
|
fveq1i |
|
258 |
|
oveq2 |
|
259 |
|
1div1e1 |
|
260 |
258 259
|
eqtrdi |
|
261 |
|
eqid |
|
262 |
|
1ex |
|
263 |
260 261 262
|
fvmpt |
|
264 |
251 263
|
ax-mp |
|
265 |
257 264
|
eqtr2i |
|
266 |
265
|
a1i |
|
267 |
|
fvres |
|
268 |
|
fvres |
|
269 |
251 268
|
mp1i |
|
270 |
|
log1 |
|
271 |
269 270
|
eqtrdi |
|
272 |
267 271
|
oveq12d |
|
273 |
93
|
sseli |
|
274 |
|
eldifsn |
|
275 |
273 274
|
sylib |
|
276 |
|
logcl |
|
277 |
275 276
|
syl |
|
278 |
277
|
subid1d |
|
279 |
272 278
|
eqtr2d |
|
280 |
279
|
oveq1d |
|
281 |
266 280
|
ifeq12d |
|
282 |
281
|
mpteq2ia |
|
283 |
256 206 282
|
dvcnp |
|
284 |
255 283
|
mpan2 |
|
285 |
240 249 224 284
|
mp3an |
|
286 |
|
oveq2 |
|
287 |
286
|
oveq2d |
|
288 |
|
eqid |
|
289 |
|
ovex |
|
290 |
287 288 289
|
fvmpt |
|
291 |
231 290
|
syl |
|
292 |
|
mul01 |
|
293 |
292
|
oveq2d |
|
294 |
293 59
|
eqtrdi |
|
295 |
291 294
|
eqtrd |
|
296 |
295
|
fveq2d |
|
297 |
285 296
|
eleqtrrid |
|
298 |
|
cnpco |
|
299 |
239 297 298
|
syl2anc |
|
300 |
204 299
|
eqeltrrd |
|
301 |
208 208 211
|
cnmptc |
|
302 |
208
|
cnmptid |
|
303 |
208 301 302 215
|
cnmpt12f |
|
304 |
|
efcn |
|
305 |
206
|
cncfcn1 |
|
306 |
304 305
|
eleqtri |
|
307 |
306
|
a1i |
|
308 |
208 303 307
|
cnmpt11f |
|
309 |
177
|
fmpttd |
|
310 |
309 231
|
ffvelrnd |
|
311 |
|
unicntop |
|
312 |
311
|
cncnpi |
|
313 |
308 310 312
|
syl2anc |
|
314 |
|
cnpco |
|
315 |
300 313 314
|
syl2anc |
|
316 |
189 315
|
eqeltrd |
|
317 |
206
|
cnfldtop |
|
318 |
317
|
a1i |
|
319 |
206
|
cnfldtopn |
|
320 |
319
|
blopn |
|
321 |
30 31 41 320
|
mp3an2i |
|
322 |
1 321
|
eqeltrid |
|
323 |
|
isopn3i |
|
324 |
317 322 323
|
sylancr |
|
325 |
231 324
|
eleqtrrd |
|
326 |
|
efcl |
|
327 |
326
|
ad2antrr |
|
328 |
84 15 86
|
sylancr |
|
329 |
328 49
|
cxpcld |
|
330 |
327 329
|
ifclda |
|
331 |
330
|
fmpttd |
|
332 |
311 311
|
cnprest |
|
333 |
318 44 325 331 332
|
syl22anc |
|
334 |
316 333
|
mpbird |
|
335 |
311
|
cnpresti |
|
336 |
4 27 334 335
|
mp3an2i |
|
337 |
25 336
|
eqeltrd |
|
338 |
|
simpl |
|
339 |
|
rpcn |
|
340 |
339
|
adantl |
|
341 |
|
rpne0 |
|
342 |
341
|
adantl |
|
343 |
338 340 342
|
divcld |
|
344 |
|
addcl |
|
345 |
84 343 344
|
sylancr |
|
346 |
345 340
|
cxpcld |
|
347 |
|
oveq2 |
|
348 |
347
|
oveq2d |
|
349 |
|
id |
|
350 |
348 349
|
oveq12d |
|
351 |
|
eqid |
|
352 |
326 346 350 206 351
|
rlimcnp3 |
|
353 |
337 352
|
mpbird |
|