Step |
Hyp |
Ref |
Expression |
1 |
|
xkococn.1 |
|
2 |
|
xkococn.s |
|
3 |
|
xkococn.k |
|
4 |
|
xkococn.c |
|
5 |
|
xkococn.v |
|
6 |
|
xkococn.a |
|
7 |
|
xkococn.b |
|
8 |
|
xkococn.i |
|
9 |
|
imacmp |
|
10 |
7 4 9
|
syl2anc |
|
11 |
2
|
adantr |
|
12 |
|
cnima |
|
13 |
6 5 12
|
syl2anc |
|
14 |
13
|
adantr |
|
15 |
|
imaco |
|
16 |
15 8
|
eqsstrrid |
|
17 |
|
eqid |
|
18 |
|
eqid |
|
19 |
17 18
|
cnf |
|
20 |
|
ffun |
|
21 |
6 19 20
|
3syl |
|
22 |
|
imassrn |
|
23 |
|
eqid |
|
24 |
23 17
|
cnf |
|
25 |
|
frn |
|
26 |
7 24 25
|
3syl |
|
27 |
22 26
|
sstrid |
|
28 |
|
fdm |
|
29 |
6 19 28
|
3syl |
|
30 |
27 29
|
sseqtrrd |
|
31 |
|
funimass3 |
|
32 |
21 30 31
|
syl2anc |
|
33 |
16 32
|
mpbid |
|
34 |
33
|
sselda |
|
35 |
|
nlly2i |
|
36 |
11 14 34 35
|
syl3anc |
|
37 |
|
nllytop |
|
38 |
2 37
|
syl |
|
39 |
38
|
ad3antrrr |
|
40 |
|
imaexg |
|
41 |
7 40
|
syl |
|
42 |
41
|
ad3antrrr |
|
43 |
|
simprl |
|
44 |
|
elrestr |
|
45 |
39 42 43 44
|
syl3anc |
|
46 |
|
simprr1 |
|
47 |
|
simpllr |
|
48 |
46 47
|
elind |
|
49 |
|
inss1 |
|
50 |
|
elpwi |
|
51 |
50
|
ad2antlr |
|
52 |
|
elssuni |
|
53 |
13 52
|
syl |
|
54 |
53
|
ad3antrrr |
|
55 |
51 54
|
sstrd |
|
56 |
|
simprr2 |
|
57 |
17
|
ssntr |
|
58 |
39 55 43 56 57
|
syl22anc |
|
59 |
49 58
|
sstrid |
|
60 |
|
simprr3 |
|
61 |
59 60
|
jca |
|
62 |
|
eleq2 |
|
63 |
|
cleq1lem |
|
64 |
62 63
|
anbi12d |
|
65 |
64
|
rspcev |
|
66 |
45 48 61 65
|
syl12anc |
|
67 |
66
|
rexlimdvaa |
|
68 |
67
|
reximdva |
|
69 |
36 68
|
mpd |
|
70 |
|
rexcom |
|
71 |
|
r19.42v |
|
72 |
71
|
rexbii |
|
73 |
70 72
|
bitri |
|
74 |
69 73
|
sylib |
|
75 |
74
|
ralrimiva |
|
76 |
17
|
restuni |
|
77 |
38 27 76
|
syl2anc |
|
78 |
77
|
raleqdv |
|
79 |
75 78
|
mpbid |
|
80 |
|
eqid |
|
81 |
|
fveq2 |
|
82 |
81
|
sseq2d |
|
83 |
|
oveq2 |
|
84 |
83
|
eleq1d |
|
85 |
82 84
|
anbi12d |
|
86 |
80 85
|
cmpcovf |
|
87 |
10 79 86
|
syl2anc |
|
88 |
77
|
adantr |
|
89 |
88
|
eqeq1d |
|
90 |
89
|
biimpar |
|
91 |
38
|
ad2antrr |
|
92 |
|
cntop2 |
|
93 |
6 92
|
syl |
|
94 |
93
|
ad2antrr |
|
95 |
|
xkotop |
|
96 |
91 94 95
|
syl2anc |
|
97 |
|
cntop1 |
|
98 |
7 97
|
syl |
|
99 |
98
|
ad2antrr |
|
100 |
|
xkotop |
|
101 |
99 91 100
|
syl2anc |
|
102 |
|
simprrl |
|
103 |
102
|
frnd |
|
104 |
|
sspwuni |
|
105 |
103 104
|
sylib |
|
106 |
13
|
ad2antrr |
|
107 |
106 52
|
syl |
|
108 |
105 107
|
sstrd |
|
109 |
|
ffn |
|
110 |
|
fniunfv |
|
111 |
102 109 110
|
3syl |
|
112 |
111
|
oveq2d |
|
113 |
|
simplr |
|
114 |
113
|
elin2d |
|
115 |
|
simprrr |
|
116 |
|
simpr |
|
117 |
116
|
ralimi |
|
118 |
115 117
|
syl |
|
119 |
17
|
fiuncmp |
|
120 |
91 114 118 119
|
syl3anc |
|
121 |
112 120
|
eqeltrrd |
|
122 |
5
|
ad2antrr |
|
123 |
17 91 94 108 121 122
|
xkoopn |
|
124 |
3
|
ad2antrr |
|
125 |
4
|
ad2antrr |
|
126 |
111 108
|
eqsstrd |
|
127 |
|
iunss |
|
128 |
126 127
|
sylib |
|
129 |
17
|
ntropn |
|
130 |
129
|
ex |
|
131 |
130
|
ralimdv |
|
132 |
91 128 131
|
sylc |
|
133 |
|
iunopn |
|
134 |
91 132 133
|
syl2anc |
|
135 |
23 99 91 124 125 134
|
xkoopn |
|
136 |
|
txopn |
|
137 |
96 101 123 135 136
|
syl22anc |
|
138 |
|
imaeq1 |
|
139 |
138
|
sseq1d |
|
140 |
6
|
ad2antrr |
|
141 |
|
imaiun |
|
142 |
111
|
imaeq2d |
|
143 |
141 142
|
syl5eqr |
|
144 |
111 105
|
eqsstrd |
|
145 |
21
|
ad2antrr |
|
146 |
102 109
|
syl |
|
147 |
29
|
ad2antrr |
|
148 |
108 147
|
sseqtrrd |
|
149 |
|
simpl1 |
|
150 |
110
|
3ad2ant2 |
|
151 |
|
simp3 |
|
152 |
150 151
|
eqsstrd |
|
153 |
|
iunss |
|
154 |
152 153
|
sylib |
|
155 |
154
|
r19.21bi |
|
156 |
|
funimass3 |
|
157 |
149 155 156
|
syl2anc |
|
158 |
157
|
ralbidva |
|
159 |
|
iunss |
|
160 |
|
iunss |
|
161 |
158 159 160
|
3bitr4g |
|
162 |
145 146 148 161
|
syl3anc |
|
163 |
144 162
|
mpbird |
|
164 |
143 163
|
eqsstrrd |
|
165 |
139 140 164
|
elrabd |
|
166 |
|
imaeq1 |
|
167 |
166
|
sseq1d |
|
168 |
7
|
ad2antrr |
|
169 |
|
simprl |
|
170 |
|
uniiun |
|
171 |
169 170
|
eqtrdi |
|
172 |
|
simpl |
|
173 |
172
|
ralimi |
|
174 |
|
ss2iun |
|
175 |
115 173 174
|
3syl |
|
176 |
171 175
|
eqsstrd |
|
177 |
167 168 176
|
elrabd |
|
178 |
165 177
|
opelxpd |
|
179 |
|
imaeq1 |
|
180 |
179
|
sseq1d |
|
181 |
180
|
elrab |
|
182 |
|
imaeq1 |
|
183 |
182
|
sseq1d |
|
184 |
183
|
elrab |
|
185 |
181 184
|
anbi12i |
|
186 |
|
simprll |
|
187 |
|
simprrl |
|
188 |
|
coeq1 |
|
189 |
|
coeq2 |
|
190 |
|
vex |
|
191 |
|
vex |
|
192 |
190 191
|
coex |
|
193 |
188 189 1 192
|
ovmpo |
|
194 |
186 187 193
|
syl2anc |
|
195 |
|
imaeq1 |
|
196 |
195
|
sseq1d |
|
197 |
|
cnco |
|
198 |
187 186 197
|
syl2anc |
|
199 |
|
imaco |
|
200 |
|
simprrr |
|
201 |
17
|
ntrss2 |
|
202 |
201
|
ex |
|
203 |
202
|
ralimdv |
|
204 |
91 128 203
|
sylc |
|
205 |
|
ss2iun |
|
206 |
204 205
|
syl |
|
207 |
206 111
|
sseqtrd |
|
208 |
207
|
adantr |
|
209 |
200 208
|
sstrd |
|
210 |
|
imass2 |
|
211 |
209 210
|
syl |
|
212 |
|
simprlr |
|
213 |
211 212
|
sstrd |
|
214 |
199 213
|
eqsstrid |
|
215 |
196 198 214
|
elrabd |
|
216 |
194 215
|
eqeltrd |
|
217 |
185 216
|
sylan2b |
|
218 |
217
|
ralrimivva |
|
219 |
1
|
mpofun |
|
220 |
|
ssrab2 |
|
221 |
|
ssrab2 |
|
222 |
|
xpss12 |
|
223 |
220 221 222
|
mp2an |
|
224 |
|
vex |
|
225 |
|
vex |
|
226 |
224 225
|
coex |
|
227 |
1 226
|
dmmpo |
|
228 |
223 227
|
sseqtrri |
|
229 |
|
funimassov |
|
230 |
219 228 229
|
mp2an |
|
231 |
218 230
|
sylibr |
|
232 |
|
funimass3 |
|
233 |
219 228 232
|
mp2an |
|
234 |
231 233
|
sylib |
|
235 |
|
eleq2 |
|
236 |
|
sseq1 |
|
237 |
235 236
|
anbi12d |
|
238 |
237
|
rspcev |
|
239 |
137 178 234 238
|
syl12anc |
|
240 |
239
|
expr |
|
241 |
240
|
exlimdv |
|
242 |
90 241
|
syldan |
|
243 |
242
|
expimpd |
|
244 |
243
|
rexlimdva |
|
245 |
87 244
|
mpd |
|