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 |
|
cvmlift2.m |
|
9 |
|
cvmlift2.a |
|
10 |
|
cvmlift2.s |
|
11 |
1 2 3 4 5 6 7
|
cvmlift2lem5 |
|
12 |
|
iunid |
|
13 |
12
|
xpeq2i |
|
14 |
|
xpiundi |
|
15 |
13 14
|
eqtr3i |
|
16 |
|
iiuni |
|
17 |
|
iiconn |
|
18 |
17
|
a1i |
|
19 |
|
inss1 |
|
20 |
|
iicmp |
|
21 |
20
|
a1i |
|
22 |
|
iitop |
|
23 |
22
|
a1i |
|
24 |
22 22
|
txtopi |
|
25 |
16
|
neiss2 |
|
26 |
22 25
|
mpan |
|
27 |
|
vex |
|
28 |
27
|
snss |
|
29 |
26 28
|
sylibr |
|
30 |
29
|
a1d |
|
31 |
30
|
rexlimiv |
|
32 |
31
|
adantl |
|
33 |
|
simpl |
|
34 |
32 33
|
jca |
|
35 |
34
|
ssopab2i |
|
36 |
|
df-xp |
|
37 |
35 10 36
|
3sstr4i |
|
38 |
22 22 16 16
|
txunii |
|
39 |
38
|
ntropn |
|
40 |
24 37 39
|
mp2an |
|
41 |
40
|
a1i |
|
42 |
2
|
adantr |
|
43 |
3
|
adantr |
|
44 |
4
|
adantr |
|
45 |
5
|
adantr |
|
46 |
|
eqid |
|
47 |
|
simprr |
|
48 |
|
simprl |
|
49 |
1 42 43 44 45 6 7 46 47 48
|
cvmlift2lem10 |
|
50 |
24
|
a1i |
|
51 |
37
|
a1i |
|
52 |
22
|
a1i |
|
53 |
|
simplrl |
|
54 |
|
simplrr |
|
55 |
|
txopn |
|
56 |
52 52 53 54 55
|
syl22anc |
|
57 |
|
simpr |
|
58 |
|
elunii |
|
59 |
58 16
|
eleqtrrdi |
|
60 |
57 54 59
|
syl2anr |
|
61 |
22
|
a1i |
|
62 |
53
|
adantr |
|
63 |
|
simprl |
|
64 |
|
opnneip |
|
65 |
61 62 63 64
|
syl3anc |
|
66 |
42
|
ad3antrrr |
|
67 |
43
|
ad3antrrr |
|
68 |
44
|
ad3antrrr |
|
69 |
45
|
ad3antrrr |
|
70 |
54
|
adantr |
|
71 |
|
simplr2 |
|
72 |
|
simprr |
|
73 |
|
sneq |
|
74 |
73
|
xpeq2d |
|
75 |
74
|
reseq2d |
|
76 |
74
|
oveq2d |
|
77 |
76
|
oveq1d |
|
78 |
75 77
|
eleq12d |
|
79 |
78
|
cbvrexvw |
|
80 |
|
simplr3 |
|
81 |
79 80
|
syl5bi |
|
82 |
1 66 67 68 69 6 7 8 62 70 71 72 81
|
cvmlift2lem11 |
|
83 |
1 66 67 68 69 6 7 8 62 70 72 71 81
|
cvmlift2lem11 |
|
84 |
82 83
|
impbid |
|
85 |
|
rspe |
|
86 |
65 84 85
|
syl2anc |
|
87 |
60 86
|
jca |
|
88 |
87
|
ex |
|
89 |
88
|
alrimivv |
|
90 |
|
df-xp |
|
91 |
90 10
|
sseq12i |
|
92 |
|
ssopab2bw |
|
93 |
91 92
|
bitri |
|
94 |
89 93
|
sylibr |
|
95 |
38
|
ssntr |
|
96 |
50 51 56 94 95
|
syl22anc |
|
97 |
|
simpr1 |
|
98 |
|
simpr2 |
|
99 |
|
opelxpi |
|
100 |
97 98 99
|
syl2anc |
|
101 |
96 100
|
sseldd |
|
102 |
101
|
ex |
|
103 |
102
|
rexlimdvva |
|
104 |
49 103
|
mpd |
|
105 |
|
vex |
|
106 |
|
opeq2 |
|
107 |
106
|
eleq1d |
|
108 |
105 107
|
ralsn |
|
109 |
104 108
|
sylibr |
|
110 |
109
|
anassrs |
|
111 |
110
|
ralrimiva |
|
112 |
|
dfss3 |
|
113 |
|
eleq1 |
|
114 |
113
|
ralxp |
|
115 |
112 114
|
bitri |
|
116 |
111 115
|
sylibr |
|
117 |
|
simpr |
|
118 |
16 16 21 23 41 116 117
|
txtube |
|
119 |
38
|
ntrss2 |
|
120 |
24 37 119
|
mp2an |
|
121 |
|
sstr |
|
122 |
120 121
|
mpan2 |
|
123 |
|
df-xp |
|
124 |
123 10
|
sseq12i |
|
125 |
|
ssopab2bw |
|
126 |
|
r2al |
|
127 |
|
ralcom |
|
128 |
125 126 127
|
3bitr2i |
|
129 |
124 128
|
bitri |
|
130 |
122 129
|
sylib |
|
131 |
|
simpr |
|
132 |
131
|
ralimi |
|
133 |
|
cvmlift2lem1 |
|
134 |
|
bicom |
|
135 |
134
|
rexbii |
|
136 |
135
|
ralbii |
|
137 |
|
cvmlift2lem1 |
|
138 |
136 137
|
sylbi |
|
139 |
133 138
|
impbid |
|
140 |
132 139
|
syl |
|
141 |
9
|
rabeq2i |
|
142 |
141
|
baib |
|
143 |
142
|
ad3antlr |
|
144 |
|
elssuni |
|
145 |
144 16
|
sseqtrrdi |
|
146 |
145
|
adantl |
|
147 |
146
|
sselda |
|
148 |
|
sneq |
|
149 |
148
|
xpeq2d |
|
150 |
149
|
sseq1d |
|
151 |
150 9
|
elrab2 |
|
152 |
151
|
baib |
|
153 |
147 152
|
syl |
|
154 |
143 153
|
bibi12d |
|
155 |
140 154
|
syl5ibr |
|
156 |
155
|
ralimdva |
|
157 |
130 156
|
syl5 |
|
158 |
157
|
anim2d |
|
159 |
158
|
reximdva |
|
160 |
118 159
|
mpd |
|
161 |
160
|
ralrimiva |
|
162 |
|
ssrab2 |
|
163 |
9 162
|
eqsstri |
|
164 |
16
|
isclo |
|
165 |
22 163 164
|
mp2an |
|
166 |
161 165
|
sylibr |
|
167 |
19 166
|
sseldi |
|
168 |
|
0elunit |
|
169 |
168
|
a1i |
|
170 |
|
relxp |
|
171 |
170
|
a1i |
|
172 |
|
opelxp |
|
173 |
|
id |
|
174 |
|
opelxpi |
|
175 |
173 169 174
|
syl2anr |
|
176 |
2
|
adantr |
|
177 |
3
|
adantr |
|
178 |
4
|
adantr |
|
179 |
5
|
adantr |
|
180 |
|
simpr |
|
181 |
168
|
a1i |
|
182 |
1 176 177 178 179 6 7 46 180 181
|
cvmlift2lem10 |
|
183 |
|
df-3an |
|
184 |
|
simprr |
|
185 |
11
|
ad3antrrr |
|
186 |
185
|
ffnd |
|
187 |
|
fnov |
|
188 |
186 187
|
sylib |
|
189 |
188
|
reseq1d |
|
190 |
|
simplrl |
|
191 |
|
elssuni |
|
192 |
191 16
|
sseqtrrdi |
|
193 |
190 192
|
syl |
|
194 |
169
|
snssd |
|
195 |
194
|
ad3antrrr |
|
196 |
|
resmpo |
|
197 |
193 195 196
|
syl2anc |
|
198 |
193
|
sselda |
|
199 |
|
simplll |
|
200 |
1 2 3 4 5 6 7
|
cvmlift2lem8 |
|
201 |
199 200
|
sylan |
|
202 |
198 201
|
syldan |
|
203 |
|
elsni |
|
204 |
203
|
oveq2d |
|
205 |
204
|
eqeq1d |
|
206 |
202 205
|
syl5ibrcom |
|
207 |
206
|
3impia |
|
208 |
207
|
mpoeq3dva |
|
209 |
189 197 208
|
3eqtrd |
|
210 |
|
eqid |
|
211 |
|
iitopon |
|
212 |
211
|
a1i |
|
213 |
|
eqid |
|
214 |
212 212
|
cnmpt1st |
|
215 |
1 2 3 4 5 6
|
cvmlift2lem2 |
|
216 |
215
|
simp1d |
|
217 |
199 216
|
syl |
|
218 |
212 212 214 217
|
cnmpt21f |
|
219 |
210 212 193 213 212 195 218
|
cnmpt2res |
|
220 |
|
vex |
|
221 |
|
snex |
|
222 |
|
txrest |
|
223 |
22 22 220 221 222
|
mp4an |
|
224 |
223
|
oveq1i |
|
225 |
219 224
|
eleqtrrdi |
|
226 |
209 225
|
eqeltrd |
|
227 |
|
sneq |
|
228 |
227
|
xpeq2d |
|
229 |
228
|
reseq2d |
|
230 |
228
|
oveq2d |
|
231 |
230
|
oveq1d |
|
232 |
229 231
|
eleq12d |
|
233 |
232
|
rspcev |
|
234 |
184 226 233
|
syl2anc |
|
235 |
|
opelxpi |
|
236 |
235
|
adantl |
|
237 |
|
simplrr |
|
238 |
237 145
|
syl |
|
239 |
|
xpss12 |
|
240 |
193 238 239
|
syl2anc |
|
241 |
38
|
restuni |
|
242 |
24 240 241
|
sylancr |
|
243 |
236 242
|
eleqtrd |
|
244 |
|
eqid |
|
245 |
244
|
cncnpi |
|
246 |
245
|
expcom |
|
247 |
243 246
|
syl |
|
248 |
24
|
a1i |
|
249 |
22
|
a1i |
|
250 |
249 249 190 237 55
|
syl22anc |
|
251 |
|
isopn3i |
|
252 |
24 250 251
|
sylancr |
|
253 |
236 252
|
eleqtrrd |
|
254 |
38 1
|
cnprest |
|
255 |
248 240 253 185 254
|
syl22anc |
|
256 |
247 255
|
sylibrd |
|
257 |
234 256
|
embantd |
|
258 |
257
|
expimpd |
|
259 |
183 258
|
syl5bi |
|
260 |
259
|
rexlimdvva |
|
261 |
182 260
|
mpd |
|
262 |
|
fveq2 |
|
263 |
262
|
eleq2d |
|
264 |
263 8
|
elrab2 |
|
265 |
175 261 264
|
sylanbrc |
|
266 |
|
elsni |
|
267 |
266
|
opeq2d |
|
268 |
267
|
eleq1d |
|
269 |
265 268
|
syl5ibrcom |
|
270 |
269
|
expimpd |
|
271 |
172 270
|
syl5bi |
|
272 |
171 271
|
relssdv |
|
273 |
|
sneq |
|
274 |
273
|
xpeq2d |
|
275 |
274
|
sseq1d |
|
276 |
275 9
|
elrab2 |
|
277 |
169 272 276
|
sylanbrc |
|
278 |
277
|
ne0d |
|
279 |
|
inss2 |
|
280 |
279 166
|
sseldi |
|
281 |
16 18 167 278 280
|
connclo |
|
282 |
281 9
|
eqtr3di |
|
283 |
|
rabid2 |
|
284 |
282 283
|
sylib |
|
285 |
|
iunss |
|
286 |
284 285
|
sylibr |
|
287 |
15 286
|
eqsstrid |
|
288 |
287 8
|
sseqtrdi |
|
289 |
|
ssrab |
|
290 |
289
|
simprbi |
|
291 |
288 290
|
syl |
|
292 |
|
txtopon |
|
293 |
211 211 292
|
mp2an |
|
294 |
|
cvmtop1 |
|
295 |
2 294
|
syl |
|
296 |
1
|
toptopon |
|
297 |
295 296
|
sylib |
|
298 |
|
cncnp |
|
299 |
293 297 298
|
sylancr |
|
300 |
11 291 299
|
mpbir2and |
|