Step |
Hyp |
Ref |
Expression |
1 |
|
radcnvrat.g |
|
2 |
|
radcnvrat.a |
|
3 |
|
radcnvrat.r |
|
4 |
|
radcnvrat.rat |
|
5 |
|
radcnvrat.z |
|
6 |
|
radcnvrat.m |
|
7 |
|
radcnvrat.n0 |
|
8 |
|
radcnvrat.l |
|
9 |
|
radcnvrat.ln0 |
|
10 |
|
xrltso |
|
11 |
10
|
a1i |
|
12 |
6
|
nn0zd |
|
13 |
5
|
reseq2i |
|
14 |
|
nn0ex |
|
15 |
14
|
mptex |
|
16 |
4 15
|
eqeltri |
|
17 |
|
climres |
|
18 |
12 16 17
|
sylancl |
|
19 |
8 18
|
mpbird |
|
20 |
13 19
|
eqbrtrid |
|
21 |
4
|
reseq1i |
|
22 |
|
eluznn0 |
|
23 |
6 22
|
sylan |
|
24 |
23
|
ex |
|
25 |
24
|
ssrdv |
|
26 |
5 25
|
eqsstrid |
|
27 |
26
|
resmptd |
|
28 |
21 27
|
syl5eq |
|
29 |
|
fvexd |
|
30 |
28 29
|
fvmpt2d |
|
31 |
5
|
peano2uzs |
|
32 |
26
|
sselda |
|
33 |
2
|
ffvelrnda |
|
34 |
32 33
|
syldan |
|
35 |
31 34
|
sylan2 |
|
36 |
26
|
sselda |
|
37 |
2
|
ffvelrnda |
|
38 |
36 37
|
syldan |
|
39 |
35 38 7
|
divcld |
|
40 |
39
|
abscld |
|
41 |
30 40
|
eqeltrd |
|
42 |
5 12 20 41
|
climrecl |
|
43 |
42 9
|
rereccld |
|
44 |
43
|
rexrd |
|
45 |
|
simpr |
|
46 |
|
elrabi |
|
47 |
43
|
adantr |
|
48 |
|
recn |
|
49 |
48
|
abscld |
|
50 |
49
|
adantl |
|
51 |
47 50
|
ltlend |
|
52 |
51
|
simplbda |
|
53 |
51
|
adantr |
|
54 |
|
simpr |
|
55 |
54
|
biantrud |
|
56 |
47 50
|
lenltd |
|
57 |
56
|
adantr |
|
58 |
53 55 57
|
3bitr2d |
|
59 |
|
1cnd |
|
60 |
50
|
recnd |
|
61 |
42
|
recnd |
|
62 |
61
|
adantr |
|
63 |
9
|
adantr |
|
64 |
59 60 62 63
|
divmul3d |
|
65 |
|
eqcom |
|
66 |
|
eqcom |
|
67 |
64 65 66
|
3bitr3g |
|
68 |
67
|
necon3bid |
|
69 |
68
|
biimpa |
|
70 |
|
1red |
|
71 |
|
fvres |
|
72 |
71
|
adantl |
|
73 |
72 41
|
eqeltrrd |
|
74 |
39
|
absge0d |
|
75 |
74 30
|
breqtrrd |
|
76 |
75 72
|
breqtrd |
|
77 |
5 12 8 73 76
|
climge0 |
|
78 |
42 77 9
|
ne0gt0d |
|
79 |
42 78
|
elrpd |
|
80 |
79
|
adantr |
|
81 |
50 70 80
|
ltmuldivd |
|
82 |
81
|
adantr |
|
83 |
|
elun |
|
84 |
|
inundif |
|
85 |
84
|
eleq2i |
|
86 |
83 85
|
bitr3i |
|
87 |
|
elin |
|
88 |
87
|
simprbi |
|
89 |
|
elsni |
|
90 |
88 89
|
syl |
|
91 |
|
fveq2 |
|
92 |
|
abs0 |
|
93 |
91 92
|
eqtrdi |
|
94 |
93
|
oveq1d |
|
95 |
61
|
mul02d |
|
96 |
94 95
|
sylan9eqr |
|
97 |
|
0lt1 |
|
98 |
96 97
|
eqbrtrdi |
|
99 |
1 2
|
radcnv0 |
|
100 |
|
eleq1 |
|
101 |
99 100
|
syl5ibrcom |
|
102 |
101
|
imp |
|
103 |
98 102
|
2thd |
|
104 |
90 103
|
sylan2 |
|
105 |
104
|
adantlr |
|
106 |
|
ax-resscn |
|
107 |
|
ssdif |
|
108 |
106 107
|
ax-mp |
|
109 |
108
|
sseli |
|
110 |
|
nn0uz |
|
111 |
6
|
ad2antrr |
|
112 |
|
fvexd |
|
113 |
|
eldifi |
|
114 |
1
|
a1i |
|
115 |
14
|
mptex |
|
116 |
115
|
a1i |
|
117 |
114 116
|
fvmpt2d |
|
118 |
117
|
adantr |
|
119 |
|
fveq2 |
|
120 |
|
oveq2 |
|
121 |
119 120
|
oveq12d |
|
122 |
121
|
adantl |
|
123 |
|
simpr |
|
124 |
|
ovexd |
|
125 |
118 122 123 124
|
fvmptd |
|
126 |
37
|
adantlr |
|
127 |
|
simplr |
|
128 |
127 123
|
expcld |
|
129 |
126 128
|
mulcld |
|
130 |
125 129
|
eqeltrd |
|
131 |
113 130
|
sylanl2 |
|
132 |
131
|
adantlr |
|
133 |
36
|
adantlr |
|
134 |
133 125
|
syldan |
|
135 |
113 134
|
sylanl2 |
|
136 |
38
|
adantlr |
|
137 |
113
|
adantl |
|
138 |
137
|
adantr |
|
139 |
36
|
adantlr |
|
140 |
138 139
|
expcld |
|
141 |
7
|
adantlr |
|
142 |
|
eldifsni |
|
143 |
142
|
ad2antlr |
|
144 |
139
|
nn0zd |
|
145 |
138 143 144
|
expne0d |
|
146 |
136 140 141 145
|
mulne0d |
|
147 |
135 146
|
eqnetrd |
|
148 |
147
|
adantlr |
|
149 |
|
fvoveq1 |
|
150 |
|
fveq2 |
|
151 |
149 150
|
oveq12d |
|
152 |
151
|
fveq2d |
|
153 |
152
|
cbvmptv |
|
154 |
5
|
reseq2i |
|
155 |
26
|
adantr |
|
156 |
155
|
resmptd |
|
157 |
154 156
|
syl5eqr |
|
158 |
12
|
adantr |
|
159 |
8
|
adantr |
|
160 |
137
|
abscld |
|
161 |
160
|
recnd |
|
162 |
14
|
mptex |
|
163 |
162
|
a1i |
|
164 |
73
|
recnd |
|
165 |
164
|
adantlr |
|
166 |
|
eqidd |
|
167 |
152
|
adantl |
|
168 |
|
fvexd |
|
169 |
166 167 139 168
|
fvmptd |
|
170 |
117
|
adantr |
|
171 |
|
simpr |
|
172 |
171
|
fveq2d |
|
173 |
171
|
oveq2d |
|
174 |
172 173
|
oveq12d |
|
175 |
|
1nn0 |
|
176 |
175
|
a1i |
|
177 |
133 176
|
nn0addcld |
|
178 |
|
ovexd |
|
179 |
170 174 177 178
|
fvmptd |
|
180 |
121
|
adantl |
|
181 |
|
ovexd |
|
182 |
170 180 133 181
|
fvmptd |
|
183 |
179 182
|
oveq12d |
|
184 |
113 183
|
sylanl2 |
|
185 |
35
|
adantlr |
|
186 |
113 177
|
sylanl2 |
|
187 |
138 186
|
expcld |
|
188 |
185 136 187 140 141 145
|
divmuldivd |
|
189 |
139
|
nn0cnd |
|
190 |
|
1cnd |
|
191 |
189 190
|
pncan2d |
|
192 |
191
|
oveq2d |
|
193 |
186
|
nn0zd |
|
194 |
138 143 144 193
|
expsubd |
|
195 |
138
|
exp1d |
|
196 |
192 194 195
|
3eqtr3d |
|
197 |
196
|
oveq2d |
|
198 |
184 188 197
|
3eqtr2d |
|
199 |
198
|
fveq2d |
|
200 |
39
|
adantlr |
|
201 |
200 138
|
absmuld |
|
202 |
169 199 201
|
3eqtrd |
|
203 |
72 30
|
eqtr3d |
|
204 |
203
|
adantlr |
|
205 |
204
|
eqcomd |
|
206 |
205
|
oveq1d |
|
207 |
161
|
adantr |
|
208 |
165 207
|
mulcomd |
|
209 |
202 206 208
|
3eqtrd |
|
210 |
5 158 159 161 163 165 209
|
climmulc2 |
|
211 |
|
climres |
|
212 |
158 162 211
|
sylancl |
|
213 |
210 212
|
mpbird |
|
214 |
157 213
|
eqbrtrrd |
|
215 |
214
|
adantr |
|
216 |
|
simpr |
|
217 |
110 5 111 112 132 148 153 215 216
|
cvgdvgrat |
|
218 |
109 217
|
sylanl2 |
|
219 |
|
eldifi |
|
220 |
|
fveq2 |
|
221 |
220
|
seqeq3d |
|
222 |
221
|
eleq1d |
|
223 |
222
|
elrab3 |
|
224 |
219 223
|
syl |
|
225 |
224
|
ad2antlr |
|
226 |
218 225
|
bitr4d |
|
227 |
226
|
an32s |
|
228 |
105 227
|
jaodan |
|
229 |
86 228
|
sylan2br |
|
230 |
229
|
an32s |
|
231 |
82 230
|
bitr3d |
|
232 |
69 231
|
syldan |
|
233 |
232
|
notbid |
|
234 |
58 233
|
bitrd |
|
235 |
234
|
biimpd |
|
236 |
235
|
impancom |
|
237 |
52 236
|
mpd |
|
238 |
237
|
ex |
|
239 |
238
|
con2d |
|
240 |
47
|
adantr |
|
241 |
|
simplr |
|
242 |
50
|
adantr |
|
243 |
|
simpr |
|
244 |
241
|
leabsd |
|
245 |
240 241 242 243 244
|
ltletrd |
|
246 |
245
|
ex |
|
247 |
239 246
|
nsyld |
|
248 |
46 247
|
sylan2 |
|
249 |
45 248
|
mpd |
|
250 |
43
|
renegcld |
|
251 |
250
|
rexrd |
|
252 |
|
iooss1 |
|
253 |
251 252
|
sylan |
|
254 |
253
|
adantlr |
|
255 |
|
eliooord |
|
256 |
255
|
simpld |
|
257 |
256
|
rgen |
|
258 |
|
ioon0 |
|
259 |
44 258
|
sylan2 |
|
260 |
259
|
ancoms |
|
261 |
260
|
biimpar |
|
262 |
|
r19.2zb |
|
263 |
261 262
|
sylib |
|
264 |
257 263
|
mpi |
|
265 |
264
|
anasss |
|
266 |
265
|
adantr |
|
267 |
|
ssrexv |
|
268 |
254 266 267
|
sylc |
|
269 |
|
simplr |
|
270 |
|
xrltnle |
|
271 |
|
xrltle |
|
272 |
270 271
|
sylbird |
|
273 |
251 272
|
sylan2 |
|
274 |
273
|
ancoms |
|
275 |
274
|
imp |
|
276 |
|
iooss1 |
|
277 |
269 275 276
|
syl2anc |
|
278 |
277
|
sselda |
|
279 |
278 256
|
syl |
|
280 |
279
|
ralrimiva |
|
281 |
42 78
|
recgt0d |
|
282 |
43 43 281 281
|
addgt0d |
|
283 |
43
|
recnd |
|
284 |
283 283
|
subnegd |
|
285 |
282 284
|
breqtrrd |
|
286 |
250 43
|
posdifd |
|
287 |
285 286
|
mpbird |
|
288 |
|
ioon0 |
|
289 |
251 44 288
|
syl2anc |
|
290 |
287 289
|
mpbird |
|
291 |
|
r19.2zb |
|
292 |
290 291
|
sylib |
|
293 |
292
|
ad2antrr |
|
294 |
280 293
|
mpd |
|
295 |
294
|
adantlrr |
|
296 |
268 295
|
pm2.61dan |
|
297 |
|
elioo2 |
|
298 |
251 44 297
|
syl2anc |
|
299 |
298
|
biimpa |
|
300 |
|
simpr |
|
301 |
300 47
|
absltd |
|
302 |
50
|
adantr |
|
303 |
|
simpr |
|
304 |
302 303
|
ltned |
|
305 |
232
|
biimpd |
|
306 |
305
|
impancom |
|
307 |
304 306
|
mpd |
|
308 |
307
|
ex |
|
309 |
301 308
|
sylbird |
|
310 |
309
|
impr |
|
311 |
310
|
expcom |
|
312 |
311
|
3impb |
|
313 |
312
|
impcom |
|
314 |
299 313
|
syldan |
|
315 |
314
|
ex |
|
316 |
315
|
ssrdv |
|
317 |
|
ssrexv |
|
318 |
316 317
|
syl |
|
319 |
318
|
adantr |
|
320 |
296 319
|
mpd |
|
321 |
11 44 249 320
|
eqsupd |
|
322 |
3 321
|
syl5eq |
|