Step |
Hyp |
Ref |
Expression |
1 |
|
tpr2rico.0 |
|
2 |
|
tpr2rico.1 |
|
3 |
|
tpr2rico.2 |
|
4 |
|
df-ioo |
|
5 |
4
|
ixxf |
|
6 |
|
ffn |
|
7 |
5 6
|
mp1i |
|
8 |
|
elssuni |
|
9 |
|
retop |
|
10 |
1 9
|
eqeltri |
|
11 |
|
uniretop |
|
12 |
1
|
unieqi |
|
13 |
11 12
|
eqtr4i |
|
14 |
10 10 13 13
|
txunii |
|
15 |
8 14
|
sseqtrrdi |
|
16 |
15
|
ad2antrr |
|
17 |
|
simplr |
|
18 |
16 17
|
sseldd |
|
19 |
|
xp1st |
|
20 |
18 19
|
syl |
|
21 |
|
simpr |
|
22 |
21
|
rpred |
|
23 |
22
|
rehalfcld |
|
24 |
20 23
|
resubcld |
|
25 |
24
|
rexrd |
|
26 |
20 23
|
readdcld |
|
27 |
26
|
rexrd |
|
28 |
|
fnovrn |
|
29 |
7 25 27 28
|
syl3anc |
|
30 |
|
xp2nd |
|
31 |
18 30
|
syl |
|
32 |
31 23
|
resubcld |
|
33 |
32
|
rexrd |
|
34 |
31 23
|
readdcld |
|
35 |
34
|
rexrd |
|
36 |
|
fnovrn |
|
37 |
7 33 35 36
|
syl3anc |
|
38 |
|
eqidd |
|
39 |
|
xpeq1 |
|
40 |
39
|
eqeq2d |
|
41 |
|
xpeq2 |
|
42 |
41
|
eqeq2d |
|
43 |
40 42
|
rspc2ev |
|
44 |
29 37 38 43
|
syl3anc |
|
45 |
|
eqid |
|
46 |
|
vex |
|
47 |
|
vex |
|
48 |
46 47
|
xpex |
|
49 |
45 48
|
elrnmpo |
|
50 |
44 49
|
sylibr |
|
51 |
50 3
|
eleqtrrdi |
|
52 |
51
|
ralrimiva |
|
53 |
|
xpss |
|
54 |
53 18
|
sseldi |
|
55 |
20
|
rexrd |
|
56 |
21
|
rphalfcld |
|
57 |
20 56
|
ltsubrpd |
|
58 |
20 56
|
ltaddrpd |
|
59 |
|
elioo1 |
|
60 |
25 27 59
|
syl2anc |
|
61 |
55 57 58 60
|
mpbir3and |
|
62 |
31
|
rexrd |
|
63 |
31 56
|
ltsubrpd |
|
64 |
31 56
|
ltaddrpd |
|
65 |
|
elioo1 |
|
66 |
33 35 65
|
syl2anc |
|
67 |
62 63 64 66
|
mpbir3and |
|
68 |
61 67
|
jca |
|
69 |
|
elxp7 |
|
70 |
54 68 69
|
sylanbrc |
|
71 |
70
|
ralrimiva |
|
72 |
|
mnfle |
|
73 |
25 72
|
syl |
|
74 |
|
pnfge |
|
75 |
27 74
|
syl |
|
76 |
|
mnfxr |
|
77 |
|
pnfxr |
|
78 |
|
ioossioo |
|
79 |
76 77 78
|
mpanl12 |
|
80 |
73 75 79
|
syl2anc |
|
81 |
|
ioomax |
|
82 |
80 81
|
sseqtrdi |
|
83 |
|
mnfle |
|
84 |
33 83
|
syl |
|
85 |
|
pnfge |
|
86 |
35 85
|
syl |
|
87 |
|
ioossioo |
|
88 |
76 77 87
|
mpanl12 |
|
89 |
84 86 88
|
syl2anc |
|
90 |
89 81
|
sseqtrdi |
|
91 |
|
xpss12 |
|
92 |
82 90 91
|
syl2anc |
|
93 |
92
|
sselda |
|
94 |
93
|
expcom |
|
95 |
94
|
ancld |
|
96 |
95
|
imdistanri |
|
97 |
15
|
adantr |
|
98 |
|
simpr1 |
|
99 |
97 98
|
sseldd |
|
100 |
99
|
3anassrs |
|
101 |
|
simpr |
|
102 |
|
simplr |
|
103 |
102
|
rphalfcld |
|
104 |
2
|
cnre2csqima |
|
105 |
100 101 103 104
|
syl3anc |
|
106 |
|
eqid |
|
107 |
2 1 106
|
cnrehmeo |
|
108 |
106
|
cnfldtopon |
|
109 |
108
|
toponunii |
|
110 |
14 109
|
hmeof1o |
|
111 |
|
f1of |
|
112 |
107 110 111
|
mp2b |
|
113 |
112
|
a1i |
|
114 |
113 100
|
ffvelrnd |
|
115 |
112
|
a1i |
|
116 |
115
|
ffvelrnda |
|
117 |
|
sqsscirc2 |
|
118 |
114 116 102 117
|
syl21anc |
|
119 |
118
|
imp |
|
120 |
102
|
rpxrd |
|
121 |
120
|
adantr |
|
122 |
|
cnxmet |
|
123 |
121 122
|
jctil |
|
124 |
114
|
adantr |
|
125 |
116
|
adantr |
|
126 |
124 125
|
jca |
|
127 |
|
eqid |
|
128 |
127
|
cnmetdval |
|
129 |
125 124 128
|
syl2anc |
|
130 |
|
simpr |
|
131 |
129 130
|
eqbrtrd |
|
132 |
|
elbl3 |
|
133 |
132
|
biimpar |
|
134 |
123 126 131 133
|
syl21anc |
|
135 |
119 134
|
syldan |
|
136 |
135
|
ex |
|
137 |
105 136
|
syld |
|
138 |
|
f1ocnv |
|
139 |
107 110 138
|
mp2b |
|
140 |
|
f1ofun |
|
141 |
139 140
|
ax-mp |
|
142 |
|
f1odm |
|
143 |
139 142
|
ax-mp |
|
144 |
116 143
|
eleqtrrdi |
|
145 |
|
funfvima |
|
146 |
141 144 145
|
sylancr |
|
147 |
107 110
|
mp1i |
|
148 |
|
f1ocnvfv1 |
|
149 |
147 101 148
|
syl2anc |
|
150 |
149
|
eleq1d |
|
151 |
150
|
biimpd |
|
152 |
137 146 151
|
3syld |
|
153 |
152
|
imp |
|
154 |
96 153
|
syl |
|
155 |
154
|
ex |
|
156 |
155
|
ssrdv |
|
157 |
156
|
ralrimiva |
|
158 |
2
|
mpofun |
|
159 |
158
|
a1i |
|
160 |
15
|
sselda |
|
161 |
|
f1odm |
|
162 |
107 110 161
|
mp2b |
|
163 |
160 162
|
eleqtrrdi |
|
164 |
|
simpr |
|
165 |
|
funfvima |
|
166 |
165
|
imp |
|
167 |
159 163 164 166
|
syl21anc |
|
168 |
|
hmeoima |
|
169 |
107 168
|
mpan |
|
170 |
106
|
cnfldtopn |
|
171 |
170
|
elmopn2 |
|
172 |
122 171
|
ax-mp |
|
173 |
172
|
simprbi |
|
174 |
169 173
|
syl |
|
175 |
174
|
adantr |
|
176 |
|
oveq1 |
|
177 |
176
|
sseq1d |
|
178 |
177
|
rexbidv |
|
179 |
178
|
rspcva |
|
180 |
167 175 179
|
syl2anc |
|
181 |
|
imass2 |
|
182 |
|
f1of1 |
|
183 |
107 110 182
|
mp2b |
|
184 |
|
f1imacnv |
|
185 |
183 15 184
|
sylancr |
|
186 |
185
|
sseq2d |
|
187 |
181 186
|
syl5ib |
|
188 |
187
|
reximdv |
|
189 |
188
|
adantr |
|
190 |
180 189
|
mpd |
|
191 |
|
r19.29 |
|
192 |
157 190 191
|
syl2anc |
|
193 |
|
sstr |
|
194 |
193
|
reximi |
|
195 |
192 194
|
syl |
|
196 |
|
r19.29 |
|
197 |
71 195 196
|
syl2anc |
|
198 |
|
r19.29 |
|
199 |
52 197 198
|
syl2anc |
|
200 |
|
eleq2 |
|
201 |
|
sseq1 |
|
202 |
200 201
|
anbi12d |
|
203 |
202
|
rspcev |
|
204 |
203
|
rexlimivw |
|
205 |
199 204
|
syl |
|