Step |
Hyp |
Ref |
Expression |
1 |
|
cvmlift2.b |
|
2 |
|
cvmlift2.f |
|
3 |
|
cvmlift2.g |
|
4 |
|
cvmlift2.p |
|
5 |
|
cvmlift2.i |
|
6 |
|
cvmlift2.h |
|
7 |
|
cvmlift2.k |
|
8 |
|
cvmlift2lem10.s |
|
9 |
|
cvmlift2lem9.1 |
|
10 |
|
cvmlift2lem9.2 |
|
11 |
|
cvmlift2lem9.3 |
|
12 |
|
cvmlift2lem9.4 |
|
13 |
|
cvmlift2lem9.5 |
|
14 |
|
cvmlift2lem9.6 |
|
15 |
|
cvmlift2lem9.7 |
|
16 |
|
cvmlift2lem9.8 |
|
17 |
|
cvmlift2lem9.9 |
|
18 |
|
cvmlift2lem9.10 |
|
19 |
|
cvmlift2lem9.11 |
|
20 |
|
cvmlift2lem9.w |
|
21 |
|
iitop |
|
22 |
|
iiuni |
|
23 |
21 21 22 22
|
txunii |
|
24 |
1 2 3 4 5 6 7
|
cvmlift2lem5 |
|
25 |
1 2 3 4 5 6 7
|
cvmlift2lem7 |
|
26 |
25 3
|
eqeltrd |
|
27 |
21 21
|
txtopi |
|
28 |
27
|
a1i |
|
29 |
|
elssuni |
|
30 |
29 22
|
sseqtrrdi |
|
31 |
11 30
|
syl |
|
32 |
31 15
|
sseldd |
|
33 |
|
elssuni |
|
34 |
33 22
|
sseqtrrdi |
|
35 |
12 34
|
syl |
|
36 |
35 16
|
sseldd |
|
37 |
|
opelxpi |
|
38 |
32 36 37
|
syl2anc |
|
39 |
24 32 36
|
fovrnd |
|
40 |
|
fvco3 |
|
41 |
24 38 40
|
syl2anc |
|
42 |
25
|
fveq1d |
|
43 |
41 42
|
eqtr3d |
|
44 |
|
df-ov |
|
45 |
44
|
fveq2i |
|
46 |
|
df-ov |
|
47 |
43 45 46
|
3eqtr4g |
|
48 |
47 9
|
eqeltrd |
|
49 |
8 1 20
|
cvmsiota |
|
50 |
2 10 39 48 49
|
syl13anc |
|
51 |
44
|
eleq1i |
|
52 |
51
|
anbi2i |
|
53 |
50 52
|
sylib |
|
54 |
|
xpss12 |
|
55 |
31 35 54
|
syl2anc |
|
56 |
|
snidg |
|
57 |
56
|
ad2antrl |
|
58 |
|
simprr |
|
59 |
|
ovres |
|
60 |
57 58 59
|
syl2anc |
|
61 |
|
eqid |
|
62 |
21
|
a1i |
|
63 |
|
snex |
|
64 |
63
|
a1i |
|
65 |
12
|
adantr |
|
66 |
|
txrest |
|
67 |
62 62 64 65 66
|
syl22anc |
|
68 |
|
iitopon |
|
69 |
31
|
sselda |
|
70 |
69
|
adantrr |
|
71 |
|
restsn2 |
|
72 |
68 70 71
|
sylancr |
|
73 |
|
pwsn |
|
74 |
|
indisconn |
|
75 |
73 74
|
eqeltri |
|
76 |
72 75
|
eqeltrdi |
|
77 |
14
|
adantr |
|
78 |
|
txconn |
|
79 |
76 77 78
|
syl2anc |
|
80 |
67 79
|
eqeltrd |
|
81 |
1 2 3 4 5 6 7
|
cvmlift2lem6 |
|
82 |
70 81
|
syldan |
|
83 |
35
|
adantr |
|
84 |
|
xpss2 |
|
85 |
83 84
|
syl |
|
86 |
70
|
snssd |
|
87 |
|
xpss1 |
|
88 |
86 87
|
syl |
|
89 |
23
|
restuni |
|
90 |
27 88 89
|
sylancr |
|
91 |
85 90
|
sseqtrd |
|
92 |
|
eqid |
|
93 |
92
|
cnrest |
|
94 |
82 91 93
|
syl2anc |
|
95 |
85
|
resabs1d |
|
96 |
27
|
a1i |
|
97 |
|
ovex |
|
98 |
63 97
|
xpex |
|
99 |
98
|
a1i |
|
100 |
|
restabs |
|
101 |
96 85 99 100
|
syl3anc |
|
102 |
101
|
oveq1d |
|
103 |
94 95 102
|
3eltr3d |
|
104 |
|
cvmtop1 |
|
105 |
2 104
|
syl |
|
106 |
105
|
adantr |
|
107 |
1
|
toptopon |
|
108 |
106 107
|
sylib |
|
109 |
|
df-ima |
|
110 |
|
simprl |
|
111 |
110
|
snssd |
|
112 |
|
xpss1 |
|
113 |
|
imass2 |
|
114 |
111 112 113
|
3syl |
|
115 |
|
imaco |
|
116 |
|
cnvco |
|
117 |
25
|
cnveqd |
|
118 |
116 117
|
syl5eqr |
|
119 |
118
|
imaeq1d |
|
120 |
115 119
|
syl5eqr |
|
121 |
17 120
|
sseqtrrd |
|
122 |
24
|
ffund |
|
123 |
24
|
fdmd |
|
124 |
55 123
|
sseqtrrd |
|
125 |
|
funimass3 |
|
126 |
122 124 125
|
syl2anc |
|
127 |
121 126
|
mpbird |
|
128 |
127
|
adantr |
|
129 |
114 128
|
sstrd |
|
130 |
109 129
|
eqsstrrid |
|
131 |
|
cnvimass |
|
132 |
|
cvmcn |
|
133 |
2 132
|
syl |
|
134 |
|
eqid |
|
135 |
1 134
|
cnf |
|
136 |
|
fdm |
|
137 |
133 135 136
|
3syl |
|
138 |
131 137
|
sseqtrid |
|
139 |
138
|
adantr |
|
140 |
|
cnrest2 |
|
141 |
108 130 139 140
|
syl3anc |
|
142 |
103 141
|
mpbid |
|
143 |
8
|
cvmsss |
|
144 |
10 143
|
syl |
|
145 |
50
|
simpld |
|
146 |
144 145
|
sseldd |
|
147 |
|
elssuni |
|
148 |
145 147
|
syl |
|
149 |
8
|
cvmsuni |
|
150 |
10 149
|
syl |
|
151 |
148 150
|
sseqtrd |
|
152 |
8
|
cvmsrcl |
|
153 |
10 152
|
syl |
|
154 |
|
cnima |
|
155 |
133 153 154
|
syl2anc |
|
156 |
|
restopn2 |
|
157 |
105 155 156
|
syl2anc |
|
158 |
146 151 157
|
mpbir2and |
|
159 |
158
|
adantr |
|
160 |
8
|
cvmscld |
|
161 |
2 10 145 160
|
syl3anc |
|
162 |
161
|
adantr |
|
163 |
18
|
adantr |
|
164 |
|
opelxpi |
|
165 |
57 163 164
|
syl2anc |
|
166 |
85 88
|
sstrd |
|
167 |
23
|
restuni |
|
168 |
27 166 167
|
sylancr |
|
169 |
165 168
|
eleqtrd |
|
170 |
|
df-ov |
|
171 |
|
ovres |
|
172 |
57 163 171
|
syl2anc |
|
173 |
|
snidg |
|
174 |
18 173
|
syl |
|
175 |
174
|
adantr |
|
176 |
|
ovres |
|
177 |
110 175 176
|
syl2anc |
|
178 |
172 177
|
eqtr4d |
|
179 |
170 178
|
syl5eqr |
|
180 |
|
eqid |
|
181 |
21
|
a1i |
|
182 |
|
snex |
|
183 |
182
|
a1i |
|
184 |
|
txrest |
|
185 |
181 181 11 183 184
|
syl22anc |
|
186 |
35 18
|
sseldd |
|
187 |
|
restsn2 |
|
188 |
68 186 187
|
sylancr |
|
189 |
|
pwsn |
|
190 |
|
indisconn |
|
191 |
189 190
|
eqeltri |
|
192 |
188 191
|
eqeltrdi |
|
193 |
|
txconn |
|
194 |
13 192 193
|
syl2anc |
|
195 |
185 194
|
eqeltrd |
|
196 |
105 107
|
sylib |
|
197 |
|
df-ima |
|
198 |
18
|
snssd |
|
199 |
|
xpss2 |
|
200 |
|
imass2 |
|
201 |
198 199 200
|
3syl |
|
202 |
201 127
|
sstrd |
|
203 |
197 202
|
eqsstrrid |
|
204 |
|
cnrest2 |
|
205 |
196 203 138 204
|
syl3anc |
|
206 |
19 205
|
mpbid |
|
207 |
|
opelxpi |
|
208 |
15 174 207
|
syl2anc |
|
209 |
186
|
snssd |
|
210 |
|
xpss12 |
|
211 |
31 209 210
|
syl2anc |
|
212 |
23
|
restuni |
|
213 |
27 211 212
|
sylancr |
|
214 |
208 213
|
eleqtrd |
|
215 |
|
df-ov |
|
216 |
|
ovres |
|
217 |
15 174 216
|
syl2anc |
|
218 |
|
snidg |
|
219 |
15 218
|
syl |
|
220 |
|
ovres |
|
221 |
219 18 220
|
syl2anc |
|
222 |
217 221
|
eqtr4d |
|
223 |
215 222
|
syl5eqr |
|
224 |
|
eqid |
|
225 |
|
snex |
|
226 |
225
|
a1i |
|
227 |
|
txrest |
|
228 |
181 181 226 12 227
|
syl22anc |
|
229 |
|
restsn2 |
|
230 |
68 32 229
|
sylancr |
|
231 |
|
pwsn |
|
232 |
|
indisconn |
|
233 |
231 232
|
eqeltri |
|
234 |
230 233
|
eqeltrdi |
|
235 |
|
txconn |
|
236 |
234 14 235
|
syl2anc |
|
237 |
228 236
|
eqeltrd |
|
238 |
1 2 3 4 5 6 7
|
cvmlift2lem6 |
|
239 |
32 238
|
mpdan |
|
240 |
|
xpss2 |
|
241 |
12 34 240
|
3syl |
|
242 |
32
|
snssd |
|
243 |
|
xpss1 |
|
244 |
242 243
|
syl |
|
245 |
23
|
restuni |
|
246 |
27 244 245
|
sylancr |
|
247 |
241 246
|
sseqtrd |
|
248 |
|
eqid |
|
249 |
248
|
cnrest |
|
250 |
239 247 249
|
syl2anc |
|
251 |
241
|
resabs1d |
|
252 |
225 97
|
xpex |
|
253 |
252
|
a1i |
|
254 |
|
restabs |
|
255 |
28 241 253 254
|
syl3anc |
|
256 |
255
|
oveq1d |
|
257 |
250 251 256
|
3eltr3d |
|
258 |
|
df-ima |
|
259 |
15
|
snssd |
|
260 |
|
xpss1 |
|
261 |
|
imass2 |
|
262 |
259 260 261
|
3syl |
|
263 |
262 127
|
sstrd |
|
264 |
258 263
|
eqsstrrid |
|
265 |
|
cnrest2 |
|
266 |
196 264 138 265
|
syl3anc |
|
267 |
257 266
|
mpbid |
|
268 |
|
opelxpi |
|
269 |
219 16 268
|
syl2anc |
|
270 |
259 260
|
syl |
|
271 |
270 55
|
sstrd |
|
272 |
23
|
restuni |
|
273 |
27 271 272
|
sylancr |
|
274 |
269 273
|
eleqtrd |
|
275 |
|
df-ov |
|
276 |
|
ovres |
|
277 |
219 16 276
|
syl2anc |
|
278 |
275 277
|
syl5eqr |
|
279 |
50
|
simprd |
|
280 |
278 279
|
eqeltrd |
|
281 |
224 237 267 158 161 274 280
|
conncn |
|
282 |
273
|
feq2d |
|
283 |
281 282
|
mpbird |
|
284 |
283 219 18
|
fovrnd |
|
285 |
223 284
|
eqeltrd |
|
286 |
180 195 206 158 161 214 285
|
conncn |
|
287 |
213
|
feq2d |
|
288 |
286 287
|
mpbird |
|
289 |
288
|
adantr |
|
290 |
289 110 175
|
fovrnd |
|
291 |
179 290
|
eqeltrd |
|
292 |
61 80 142 159 162 169 291
|
conncn |
|
293 |
168
|
feq2d |
|
294 |
292 293
|
mpbird |
|
295 |
294 57 58
|
fovrnd |
|
296 |
60 295
|
eqeltrrd |
|
297 |
296
|
ralrimivva |
|
298 |
|
funimassov |
|
299 |
122 124 298
|
syl2anc |
|
300 |
297 299
|
mpbird |
|
301 |
1 23 8 2 24 26 28 38 10 53 55 300
|
cvmlift2lem9a |
|