Step |
Hyp |
Ref |
Expression |
1 |
|
dvadd.f |
|
2 |
|
dvadd.x |
|
3 |
|
dvadd.g |
|
4 |
|
dvadd.y |
|
5 |
|
dvaddbr.s |
|
6 |
|
dvadd.bf |
|
7 |
|
dvadd.bg |
|
8 |
|
dvadd.j |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
9 8 10 5 1 2
|
eldv |
|
12 |
6 11
|
mpbid |
|
13 |
12
|
simpld |
|
14 |
|
eqid |
|
15 |
9 8 14 5 3 4
|
eldv |
|
16 |
7 15
|
mpbid |
|
17 |
16
|
simpld |
|
18 |
13 17
|
elind |
|
19 |
8
|
cnfldtopon |
|
20 |
|
resttopon |
|
21 |
19 5 20
|
sylancr |
|
22 |
|
topontop |
|
23 |
21 22
|
syl |
|
24 |
|
toponuni |
|
25 |
21 24
|
syl |
|
26 |
2 25
|
sseqtrd |
|
27 |
4 25
|
sseqtrd |
|
28 |
|
eqid |
|
29 |
28
|
ntrin |
|
30 |
23 26 27 29
|
syl3anc |
|
31 |
18 30
|
eleqtrrd |
|
32 |
1
|
adantr |
|
33 |
|
inss1 |
|
34 |
|
eldifi |
|
35 |
34
|
adantl |
|
36 |
33 35
|
sselid |
|
37 |
32 36
|
ffvelcdmd |
|
38 |
5 1 2
|
dvbss |
|
39 |
|
reldv |
|
40 |
|
releldm |
|
41 |
39 6 40
|
sylancr |
|
42 |
38 41
|
sseldd |
|
43 |
1 42
|
ffvelcdmd |
|
44 |
43
|
adantr |
|
45 |
37 44
|
subcld |
|
46 |
2 5
|
sstrd |
|
47 |
46
|
adantr |
|
48 |
47 36
|
sseldd |
|
49 |
46 42
|
sseldd |
|
50 |
49
|
adantr |
|
51 |
48 50
|
subcld |
|
52 |
|
eldifsni |
|
53 |
52
|
adantl |
|
54 |
48 50 53
|
subne0d |
|
55 |
45 51 54
|
divcld |
|
56 |
3
|
adantr |
|
57 |
|
inss2 |
|
58 |
57 35
|
sselid |
|
59 |
56 58
|
ffvelcdmd |
|
60 |
55 59
|
mulcld |
|
61 |
|
ssdif |
|
62 |
57 61
|
mp1i |
|
63 |
62
|
sselda |
|
64 |
4 5
|
sstrd |
|
65 |
5 3 4
|
dvbss |
|
66 |
|
reldv |
|
67 |
|
releldm |
|
68 |
66 7 67
|
sylancr |
|
69 |
65 68
|
sseldd |
|
70 |
3 64 69
|
dvlem |
|
71 |
63 70
|
syldan |
|
72 |
71 44
|
mulcld |
|
73 |
|
ssidd |
|
74 |
|
txtopon |
|
75 |
19 19 74
|
mp2an |
|
76 |
75
|
toponrestid |
|
77 |
12
|
simprd |
|
78 |
1 46 42
|
dvlem |
|
79 |
78
|
fmpttd |
|
80 |
|
ssdif |
|
81 |
33 80
|
mp1i |
|
82 |
46
|
ssdifssd |
|
83 |
|
eqid |
|
84 |
33 2
|
sstrid |
|
85 |
84 25
|
sseqtrd |
|
86 |
|
difssd |
|
87 |
85 86
|
unssd |
|
88 |
|
ssun1 |
|
89 |
88
|
a1i |
|
90 |
28
|
ntrss |
|
91 |
23 87 89 90
|
syl3anc |
|
92 |
91 31
|
sseldd |
|
93 |
92 42
|
elind |
|
94 |
33
|
a1i |
|
95 |
|
eqid |
|
96 |
28 95
|
restntr |
|
97 |
23 26 94 96
|
syl3anc |
|
98 |
8
|
cnfldtop |
|
99 |
98
|
a1i |
|
100 |
|
cnex |
|
101 |
|
ssexg |
|
102 |
5 100 101
|
sylancl |
|
103 |
|
restabs |
|
104 |
99 2 102 103
|
syl3anc |
|
105 |
104
|
fveq2d |
|
106 |
105
|
fveq1d |
|
107 |
97 106
|
eqtr3d |
|
108 |
93 107
|
eleqtrd |
|
109 |
|
undif1 |
|
110 |
42
|
snssd |
|
111 |
|
ssequn2 |
|
112 |
110 111
|
sylib |
|
113 |
109 112
|
eqtrid |
|
114 |
113
|
oveq2d |
|
115 |
114
|
fveq2d |
|
116 |
|
undif1 |
|
117 |
42 69
|
elind |
|
118 |
117
|
snssd |
|
119 |
|
ssequn2 |
|
120 |
118 119
|
sylib |
|
121 |
116 120
|
eqtrid |
|
122 |
115 121
|
fveq12d |
|
123 |
108 122
|
eleqtrrd |
|
124 |
79 81 82 8 83 123
|
limcres |
|
125 |
81
|
resmptd |
|
126 |
125
|
oveq1d |
|
127 |
124 126
|
eqtr3d |
|
128 |
77 127
|
eleqtrd |
|
129 |
|
eqid |
|
130 |
129 8
|
dvcnp2 |
|
131 |
5 3 4 68 130
|
syl31anc |
|
132 |
8 129
|
cnplimc |
|
133 |
64 69 132
|
syl2anc |
|
134 |
131 133
|
mpbid |
|
135 |
134
|
simprd |
|
136 |
|
difss |
|
137 |
136 57
|
sstri |
|
138 |
137
|
a1i |
|
139 |
|
eqid |
|
140 |
|
difssd |
|
141 |
85 140
|
unssd |
|
142 |
|
ssun1 |
|
143 |
142
|
a1i |
|
144 |
28
|
ntrss |
|
145 |
23 141 143 144
|
syl3anc |
|
146 |
145 31
|
sseldd |
|
147 |
146 69
|
elind |
|
148 |
57
|
a1i |
|
149 |
|
eqid |
|
150 |
28 149
|
restntr |
|
151 |
23 27 148 150
|
syl3anc |
|
152 |
|
restabs |
|
153 |
99 4 102 152
|
syl3anc |
|
154 |
153
|
fveq2d |
|
155 |
154
|
fveq1d |
|
156 |
151 155
|
eqtr3d |
|
157 |
147 156
|
eleqtrd |
|
158 |
69
|
snssd |
|
159 |
|
ssequn2 |
|
160 |
158 159
|
sylib |
|
161 |
160
|
oveq2d |
|
162 |
161
|
fveq2d |
|
163 |
162 121
|
fveq12d |
|
164 |
157 163
|
eleqtrrd |
|
165 |
3 138 64 8 139 164
|
limcres |
|
166 |
3 138
|
feqresmpt |
|
167 |
166
|
oveq1d |
|
168 |
165 167
|
eqtr3d |
|
169 |
135 168
|
eleqtrd |
|
170 |
8
|
mulcn |
|
171 |
5 1 2
|
dvcl |
|
172 |
6 171
|
mpdan |
|
173 |
3 69
|
ffvelcdmd |
|
174 |
172 173
|
opelxpd |
|
175 |
75
|
toponunii |
|
176 |
175
|
cncnpi |
|
177 |
170 174 176
|
sylancr |
|
178 |
55 59 73 73 8 76 128 169 177
|
limccnp2 |
|
179 |
16
|
simprd |
|
180 |
70
|
fmpttd |
|
181 |
64
|
ssdifssd |
|
182 |
|
eqid |
|
183 |
|
undif1 |
|
184 |
183 160
|
eqtrid |
|
185 |
184
|
oveq2d |
|
186 |
185
|
fveq2d |
|
187 |
186 121
|
fveq12d |
|
188 |
157 187
|
eleqtrrd |
|
189 |
180 62 181 8 182 188
|
limcres |
|
190 |
62
|
resmptd |
|
191 |
190
|
oveq1d |
|
192 |
189 191
|
eqtr3d |
|
193 |
179 192
|
eleqtrd |
|
194 |
84 5
|
sstrd |
|
195 |
|
cncfmptc |
|
196 |
43 194 73 195
|
syl3anc |
|
197 |
|
eqidd |
|
198 |
196 117 197
|
cnmptlimc |
|
199 |
43
|
adantr |
|
200 |
199
|
fmpttd |
|
201 |
200
|
limcdif |
|
202 |
|
resmpt |
|
203 |
136 202
|
mp1i |
|
204 |
203
|
oveq1d |
|
205 |
201 204
|
eqtrd |
|
206 |
198 205
|
eleqtrd |
|
207 |
5 3 4
|
dvcl |
|
208 |
7 207
|
mpdan |
|
209 |
208 43
|
opelxpd |
|
210 |
175
|
cncnpi |
|
211 |
170 209 210
|
sylancr |
|
212 |
71 44 73 73 8 76 193 206 211
|
limccnp2 |
|
213 |
8
|
addcn |
|
214 |
172 173
|
mulcld |
|
215 |
208 43
|
mulcld |
|
216 |
214 215
|
opelxpd |
|
217 |
175
|
cncnpi |
|
218 |
213 216 217
|
sylancr |
|
219 |
60 72 73 73 8 76 178 212 218
|
limccnp2 |
|
220 |
42
|
adantr |
|
221 |
32 220
|
ffvelcdmd |
|
222 |
37 221
|
subcld |
|
223 |
222 59
|
mulcld |
|
224 |
69
|
adantr |
|
225 |
56 224
|
ffvelcdmd |
|
226 |
59 225
|
subcld |
|
227 |
226 221
|
mulcld |
|
228 |
47 220
|
sseldd |
|
229 |
48 228
|
subcld |
|
230 |
223 227 229 54
|
divdird |
|
231 |
37 59
|
mulcld |
|
232 |
221 59
|
mulcld |
|
233 |
221 225
|
mulcld |
|
234 |
231 232 233
|
npncand |
|
235 |
37 221 59
|
subdird |
|
236 |
226 221
|
mulcomd |
|
237 |
221 59 225
|
subdid |
|
238 |
236 237
|
eqtrd |
|
239 |
235 238
|
oveq12d |
|
240 |
1
|
ffnd |
|
241 |
240
|
adantr |
|
242 |
3
|
ffnd |
|
243 |
242
|
adantr |
|
244 |
|
ssexg |
|
245 |
46 100 244
|
sylancl |
|
246 |
245
|
adantr |
|
247 |
|
ssexg |
|
248 |
64 100 247
|
sylancl |
|
249 |
248
|
adantr |
|
250 |
|
eqid |
|
251 |
|
eqidd |
|
252 |
|
eqidd |
|
253 |
241 243 246 249 250 251 252
|
ofval |
|
254 |
35 253
|
mpdan |
|
255 |
|
eqidd |
|
256 |
|
eqidd |
|
257 |
241 243 246 249 250 255 256
|
ofval |
|
258 |
117 257
|
mpidan |
|
259 |
254 258
|
oveq12d |
|
260 |
234 239 259
|
3eqtr4d |
|
261 |
260
|
oveq1d |
|
262 |
222 59 229 54
|
div23d |
|
263 |
226 221 229 54
|
div23d |
|
264 |
262 263
|
oveq12d |
|
265 |
230 261 264
|
3eqtr3d |
|
266 |
265
|
mpteq2dva |
|
267 |
266
|
oveq1d |
|
268 |
219 267
|
eleqtrrd |
|
269 |
|
eqid |
|
270 |
|
mulcl |
|
271 |
270
|
adantl |
|
272 |
271 1 3 245 248 250
|
off |
|
273 |
9 8 269 5 272 84
|
eldv |
|
274 |
31 268 273
|
mpbir2and |
|