Step |
Hyp |
Ref |
Expression |
1 |
|
cncfiooicclem1.x |
|
2 |
|
cncfiooicclem1.g |
|
3 |
|
cncfiooicclem1.a |
|
4 |
|
cncfiooicclem1.b |
|
5 |
|
cncfiooicclem1.altb |
|
6 |
|
cncfiooicclem1.f |
|
7 |
|
cncfiooicclem1.l |
|
8 |
|
cncfiooicclem1.r |
|
9 |
|
limccl |
|
10 |
9 8
|
sseldi |
|
11 |
10
|
ad2antrr |
|
12 |
|
limccl |
|
13 |
12 7
|
sseldi |
|
14 |
13
|
ad3antrrr |
|
15 |
|
simplll |
|
16 |
|
orel1 |
|
17 |
16
|
con3dimp |
|
18 |
|
vex |
|
19 |
18
|
elpr |
|
20 |
17 19
|
sylnibr |
|
21 |
20
|
adantll |
|
22 |
|
simpllr |
|
23 |
3
|
rexrd |
|
24 |
15 23
|
syl |
|
25 |
4
|
rexrd |
|
26 |
15 25
|
syl |
|
27 |
3 4 5
|
ltled |
|
28 |
15 27
|
syl |
|
29 |
|
prunioo |
|
30 |
24 26 28 29
|
syl3anc |
|
31 |
22 30
|
eleqtrrd |
|
32 |
|
elun |
|
33 |
31 32
|
sylib |
|
34 |
|
orel2 |
|
35 |
21 33 34
|
sylc |
|
36 |
|
cncff |
|
37 |
6 36
|
syl |
|
38 |
37
|
ffvelrnda |
|
39 |
15 35 38
|
syl2anc |
|
40 |
14 39
|
ifclda |
|
41 |
11 40
|
ifclda |
|
42 |
1 41 2
|
fmptdf |
|
43 |
|
elun |
|
44 |
23 25 27 29
|
syl3anc |
|
45 |
44
|
eleq2d |
|
46 |
43 45
|
bitr3id |
|
47 |
46
|
biimpar |
|
48 |
|
ioossicc |
|
49 |
|
fssres |
|
50 |
42 48 49
|
sylancl |
|
51 |
50
|
feqmptd |
|
52 |
|
nfmpt1 |
|
53 |
2 52
|
nfcxfr |
|
54 |
|
nfcv |
|
55 |
53 54
|
nfres |
|
56 |
|
nfcv |
|
57 |
55 56
|
nffv |
|
58 |
|
nfcv |
|
59 |
|
nfcv |
|
60 |
58 59
|
nffv |
|
61 |
|
fveq2 |
|
62 |
57 60 61
|
cbvmpt |
|
63 |
62
|
a1i |
|
64 |
|
fvres |
|
65 |
64
|
adantl |
|
66 |
|
simpr |
|
67 |
48 66
|
sseldi |
|
68 |
10
|
adantr |
|
69 |
13
|
ad2antrr |
|
70 |
38
|
adantr |
|
71 |
69 70
|
ifclda |
|
72 |
68 71
|
ifcld |
|
73 |
2
|
fvmpt2 |
|
74 |
67 72 73
|
syl2anc |
|
75 |
|
elioo4g |
|
76 |
75
|
biimpi |
|
77 |
76
|
simpld |
|
78 |
77
|
simp1d |
|
79 |
|
elioore |
|
80 |
79
|
rexrd |
|
81 |
|
eliooord |
|
82 |
81
|
simpld |
|
83 |
|
xrltne |
|
84 |
78 80 82 83
|
syl3anc |
|
85 |
84
|
adantl |
|
86 |
85
|
neneqd |
|
87 |
86
|
iffalsed |
|
88 |
81
|
simprd |
|
89 |
79 88
|
ltned |
|
90 |
89
|
neneqd |
|
91 |
90
|
iffalsed |
|
92 |
91
|
adantl |
|
93 |
87 92
|
eqtrd |
|
94 |
65 74 93
|
3eqtrd |
|
95 |
1 94
|
mpteq2da |
|
96 |
51 63 95
|
3eqtrd |
|
97 |
37
|
feqmptd |
|
98 |
|
ioosscn |
|
99 |
98
|
a1i |
|
100 |
|
ssid |
|
101 |
|
eqid |
|
102 |
|
eqid |
|
103 |
101
|
cnfldtop |
|
104 |
|
unicntop |
|
105 |
104
|
restid |
|
106 |
103 105
|
ax-mp |
|
107 |
106
|
eqcomi |
|
108 |
101 102 107
|
cncfcn |
|
109 |
99 100 108
|
sylancl |
|
110 |
6 97 109
|
3eltr3d |
|
111 |
96 110
|
eqeltrd |
|
112 |
104
|
restuni |
|
113 |
103 98 112
|
mp2an |
|
114 |
113
|
cncnpi |
|
115 |
111 114
|
sylan |
|
116 |
103
|
a1i |
|
117 |
48
|
a1i |
|
118 |
|
ovex |
|
119 |
118
|
a1i |
|
120 |
|
restabs |
|
121 |
116 117 119 120
|
syl3anc |
|
122 |
121
|
eqcomd |
|
123 |
122
|
oveq1d |
|
124 |
123
|
fveq1d |
|
125 |
115 124
|
eleqtrd |
|
126 |
|
resttop |
|
127 |
103 118 126
|
mp2an |
|
128 |
127
|
a1i |
|
129 |
48
|
a1i |
|
130 |
3 4
|
iccssred |
|
131 |
|
ax-resscn |
|
132 |
130 131
|
sstrdi |
|
133 |
104
|
restuni |
|
134 |
103 132 133
|
sylancr |
|
135 |
129 134
|
sseqtrd |
|
136 |
135
|
adantr |
|
137 |
|
retop |
|
138 |
137
|
a1i |
|
139 |
|
ioossre |
|
140 |
|
difss |
|
141 |
139 140
|
unssi |
|
142 |
141
|
a1i |
|
143 |
|
ssun1 |
|
144 |
143
|
a1i |
|
145 |
|
uniretop |
|
146 |
145
|
ntrss |
|
147 |
138 142 144 146
|
syl3anc |
|
148 |
|
simpr |
|
149 |
|
ioontr |
|
150 |
148 149
|
eleqtrrdi |
|
151 |
147 150
|
sseldd |
|
152 |
48 148
|
sseldi |
|
153 |
151 152
|
elind |
|
154 |
130
|
adantr |
|
155 |
|
eqid |
|
156 |
145 155
|
restntr |
|
157 |
138 154 117 156
|
syl3anc |
|
158 |
153 157
|
eleqtrrd |
|
159 |
101
|
tgioo2 |
|
160 |
159
|
a1i |
|
161 |
160
|
oveq1d |
|
162 |
103
|
a1i |
|
163 |
|
reex |
|
164 |
163
|
a1i |
|
165 |
|
restabs |
|
166 |
162 130 164 165
|
syl3anc |
|
167 |
161 166
|
eqtrd |
|
168 |
167
|
fveq2d |
|
169 |
168
|
fveq1d |
|
170 |
169
|
adantr |
|
171 |
158 170
|
eleqtrd |
|
172 |
134
|
feq2d |
|
173 |
42 172
|
mpbid |
|
174 |
173
|
adantr |
|
175 |
|
eqid |
|
176 |
175 104
|
cnprest |
|
177 |
128 136 171 174 176
|
syl22anc |
|
178 |
125 177
|
mpbird |
|
179 |
|
elpri |
|
180 |
|
iftrue |
|
181 |
|
lbicc2 |
|
182 |
23 25 27 181
|
syl3anc |
|
183 |
2 180 182 8
|
fvmptd3 |
|
184 |
97
|
eqcomd |
|
185 |
96 184
|
eqtr2d |
|
186 |
185
|
oveq1d |
|
187 |
8 186
|
eleqtrd |
|
188 |
3 4 5 42
|
limciccioolb |
|
189 |
187 188
|
eleqtrd |
|
190 |
183 189
|
eqeltrd |
|
191 |
|
eqid |
|
192 |
101 191
|
cnplimc |
|
193 |
132 182 192
|
syl2anc |
|
194 |
42 190 193
|
mpbir2and |
|
195 |
194
|
adantr |
|
196 |
|
fveq2 |
|
197 |
196
|
eqcomd |
|
198 |
197
|
adantl |
|
199 |
195 198
|
eleqtrd |
|
200 |
180
|
adantl |
|
201 |
|
eqtr2 |
|
202 |
|
iftrue |
|
203 |
202
|
eqcomd |
|
204 |
201 203
|
syl |
|
205 |
200 204
|
eqtrd |
|
206 |
|
iffalse |
|
207 |
206
|
adantl |
|
208 |
|
iftrue |
|
209 |
208
|
adantr |
|
210 |
|
df-ne |
|
211 |
|
pm13.18 |
|
212 |
210 211
|
sylan2br |
|
213 |
212
|
neneqd |
|
214 |
213
|
iffalsed |
|
215 |
|
eqid |
|
216 |
215
|
iftruei |
|
217 |
214 216
|
eqtr2di |
|
218 |
207 209 217
|
3eqtrd |
|
219 |
205 218
|
pm2.61dan |
|
220 |
4
|
leidd |
|
221 |
3 4 4 27 220
|
eliccd |
|
222 |
216 13
|
eqeltrid |
|
223 |
10 222
|
ifcld |
|
224 |
2 219 221 223
|
fvmptd3 |
|
225 |
3 5
|
gtned |
|
226 |
225
|
neneqd |
|
227 |
226
|
iffalsed |
|
228 |
216
|
a1i |
|
229 |
224 227 228
|
3eqtrd |
|
230 |
185
|
oveq1d |
|
231 |
7 230
|
eleqtrd |
|
232 |
3 4 5 42
|
limcicciooub |
|
233 |
231 232
|
eleqtrd |
|
234 |
229 233
|
eqeltrd |
|
235 |
101 191
|
cnplimc |
|
236 |
132 221 235
|
syl2anc |
|
237 |
42 234 236
|
mpbir2and |
|
238 |
237
|
adantr |
|
239 |
|
fveq2 |
|
240 |
239
|
eqcomd |
|
241 |
240
|
adantl |
|
242 |
238 241
|
eleqtrd |
|
243 |
199 242
|
jaodan |
|
244 |
179 243
|
sylan2 |
|
245 |
178 244
|
jaodan |
|
246 |
47 245
|
syldan |
|
247 |
246
|
ralrimiva |
|
248 |
101
|
cnfldtopon |
|
249 |
|
resttopon |
|
250 |
248 132 249
|
sylancr |
|
251 |
|
cncnp |
|
252 |
250 248 251
|
sylancl |
|
253 |
42 247 252
|
mpbir2and |
|
254 |
101 191 107
|
cncfcn |
|
255 |
132 100 254
|
sylancl |
|
256 |
253 255
|
eleqtrrd |
|