Step |
Hyp |
Ref |
Expression |
1 |
|
poimir.0 |
|
2 |
|
poimir.i |
|
3 |
|
poimir.r |
|
4 |
|
broucube.1 |
|
5 |
|
elmapfn |
|
6 |
5 2
|
eleq2s |
|
7 |
6
|
adantl |
|
8 |
|
ovex |
|
9 |
|
retopon |
|
10 |
3
|
pttoponconst |
|
11 |
8 9 10
|
mp2an |
|
12 |
|
reex |
|
13 |
|
unitssre |
|
14 |
|
mapss |
|
15 |
12 13 14
|
mp2an |
|
16 |
2 15
|
eqsstri |
|
17 |
|
resttopon |
|
18 |
11 16 17
|
mp2an |
|
19 |
18
|
toponunii |
|
20 |
19 19
|
cnf |
|
21 |
4 20
|
syl |
|
22 |
21
|
ffvelrnda |
|
23 |
|
elmapfn |
|
24 |
23 2
|
eleq2s |
|
25 |
22 24
|
syl |
|
26 |
|
ovexd |
|
27 |
|
inidm |
|
28 |
|
eqidd |
|
29 |
|
eqidd |
|
30 |
7 25 26 26 27 28 29
|
offval |
|
31 |
30
|
mpteq2dva |
|
32 |
18
|
a1i |
|
33 |
|
ovexd |
|
34 |
|
retop |
|
35 |
34
|
fconst6 |
|
36 |
35
|
a1i |
|
37 |
18
|
a1i |
|
38 |
|
eqid |
|
39 |
38
|
cnfldtop |
|
40 |
|
cnrest2r |
|
41 |
39 40
|
ax-mp |
|
42 |
|
resmpt |
|
43 |
16 42
|
ax-mp |
|
44 |
11
|
toponunii |
|
45 |
44 3
|
ptpjcn |
|
46 |
8 35 45
|
mp3an12 |
|
47 |
44
|
cnrest |
|
48 |
46 16 47
|
sylancl |
|
49 |
43 48
|
eqeltrrid |
|
50 |
|
fvex |
|
51 |
50
|
fvconst2 |
|
52 |
38
|
tgioo2 |
|
53 |
51 52
|
eqtrdi |
|
54 |
53
|
oveq2d |
|
55 |
49 54
|
eleqtrd |
|
56 |
41 55
|
sseldi |
|
57 |
56
|
adantl |
|
58 |
21
|
feqmptd |
|
59 |
58 4
|
eqeltrrd |
|
60 |
59
|
adantr |
|
61 |
|
fveq1 |
|
62 |
61
|
cbvmptv |
|
63 |
62 57
|
eqeltrrid |
|
64 |
|
fveq1 |
|
65 |
37 60 37 63 64
|
cnmpt11 |
|
66 |
38
|
subcn |
|
67 |
66
|
a1i |
|
68 |
37 57 65 67
|
cnmpt12f |
|
69 |
|
elmapi |
|
70 |
69 2
|
eleq2s |
|
71 |
70
|
ffvelrnda |
|
72 |
13 71
|
sseldi |
|
73 |
72
|
adantll |
|
74 |
|
elmapi |
|
75 |
74 2
|
eleq2s |
|
76 |
22 75
|
syl |
|
77 |
76
|
ffvelrnda |
|
78 |
13 77
|
sseldi |
|
79 |
73 78
|
resubcld |
|
80 |
79
|
an32s |
|
81 |
80
|
fmpttd |
|
82 |
|
frn |
|
83 |
38
|
cnfldtopon |
|
84 |
|
ax-resscn |
|
85 |
|
cnrest2 |
|
86 |
83 84 85
|
mp3an13 |
|
87 |
81 82 86
|
3syl |
|
88 |
68 87
|
mpbid |
|
89 |
54
|
adantl |
|
90 |
88 89
|
eleqtrrd |
|
91 |
3 32 33 36 90
|
ptcn |
|
92 |
31 91
|
eqeltrd |
|
93 |
|
simpr2 |
|
94 |
|
id |
|
95 |
|
fveq2 |
|
96 |
94 95
|
oveq12d |
|
97 |
|
eqid |
|
98 |
|
ovex |
|
99 |
96 97 98
|
fvmpt |
|
100 |
99
|
fveq1d |
|
101 |
93 100
|
syl |
|
102 |
|
elmapfn |
|
103 |
102 2
|
eleq2s |
|
104 |
103
|
adantl |
|
105 |
21
|
ffvelrnda |
|
106 |
|
elmapfn |
|
107 |
106 2
|
eleq2s |
|
108 |
105 107
|
syl |
|
109 |
108
|
adantlr |
|
110 |
|
ovexd |
|
111 |
|
simpllr |
|
112 |
|
eqidd |
|
113 |
104 109 110 110 27 111 112
|
ofval |
|
114 |
|
df-neg |
|
115 |
113 114
|
eqtr4di |
|
116 |
115
|
exp41 |
|
117 |
116
|
com24 |
|
118 |
117
|
3imp2 |
|
119 |
101 118
|
eqtrd |
|
120 |
|
elmapi |
|
121 |
120 2
|
eleq2s |
|
122 |
105 121
|
syl |
|
123 |
122
|
ffvelrnda |
|
124 |
|
0xr |
|
125 |
|
1xr |
|
126 |
|
iccgelb |
|
127 |
124 125 126
|
mp3an12 |
|
128 |
123 127
|
syl |
|
129 |
13 123
|
sseldi |
|
130 |
129
|
le0neg2d |
|
131 |
128 130
|
mpbid |
|
132 |
131
|
an32s |
|
133 |
132
|
anasss |
|
134 |
133
|
3adantr3 |
|
135 |
119 134
|
eqbrtrd |
|
136 |
|
iccleub |
|
137 |
124 125 136
|
mp3an12 |
|
138 |
123 137
|
syl |
|
139 |
|
1red |
|
140 |
139 129
|
subge0d |
|
141 |
138 140
|
mpbird |
|
142 |
141
|
an32s |
|
143 |
142
|
anasss |
|
144 |
143
|
3adantr3 |
|
145 |
|
simpr2 |
|
146 |
145 100
|
syl |
|
147 |
103
|
adantl |
|
148 |
108
|
adantlr |
|
149 |
|
ovexd |
|
150 |
|
simpllr |
|
151 |
|
eqidd |
|
152 |
147 148 149 149 27 150 151
|
ofval |
|
153 |
152
|
exp41 |
|
154 |
153
|
com24 |
|
155 |
154
|
3imp2 |
|
156 |
146 155
|
eqtrd |
|
157 |
144 156
|
breqtrrd |
|
158 |
1 2 3 92 135 157
|
poimir |
|
159 |
|
id |
|
160 |
|
fveq2 |
|
161 |
159 160
|
oveq12d |
|
162 |
|
ovex |
|
163 |
161 97 162
|
fvmpt |
|
164 |
163
|
adantl |
|
165 |
164
|
eqeq1d |
|
166 |
|
elmapfn |
|
167 |
166 2
|
eleq2s |
|
168 |
167
|
adantl |
|
169 |
21
|
ffvelrnda |
|
170 |
|
elmapfn |
|
171 |
170 2
|
eleq2s |
|
172 |
169 171
|
syl |
|
173 |
|
ovexd |
|
174 |
|
eqidd |
|
175 |
|
eqidd |
|
176 |
168 172 173 173 27 174 175
|
ofval |
|
177 |
|
c0ex |
|
178 |
177
|
fvconst2 |
|
179 |
178
|
adantl |
|
180 |
176 179
|
eqeq12d |
|
181 |
13 84
|
sstri |
|
182 |
|
elmapi |
|
183 |
182 2
|
eleq2s |
|
184 |
183
|
ffvelrnda |
|
185 |
181 184
|
sseldi |
|
186 |
185
|
adantll |
|
187 |
|
elmapi |
|
188 |
187 2
|
eleq2s |
|
189 |
169 188
|
syl |
|
190 |
189
|
ffvelrnda |
|
191 |
181 190
|
sseldi |
|
192 |
186 191
|
subeq0ad |
|
193 |
180 192
|
bitrd |
|
194 |
193
|
ralbidva |
|
195 |
168 172 173 173 27
|
offn |
|
196 |
|
fnconstg |
|
197 |
177 196
|
ax-mp |
|
198 |
|
eqfnfv |
|
199 |
195 197 198
|
sylancl |
|
200 |
|
eqfnfv |
|
201 |
168 172 200
|
syl2anc |
|
202 |
194 199 201
|
3bitr4d |
|
203 |
165 202
|
bitrd |
|
204 |
203
|
rexbidva |
|
205 |
158 204
|
mpbid |
|