Step |
Hyp |
Ref |
Expression |
1 |
|
ioorrnopnlem.x |
|
2 |
|
ioorrnopnlem.n |
|
3 |
|
ioorrnopnlem.a |
|
4 |
|
ioorrnopnlem.b |
|
5 |
|
ioorrnopnlem.f |
|
6 |
|
ioorrnopnlem.h |
|
7 |
|
ioorrnopnlem.e |
|
8 |
|
ioorrnopnlem.v |
|
9 |
|
ioorrnopnlem.d |
|
10 |
1 9
|
rrndsxmet |
|
11 |
|
nfv |
|
12 |
|
reex |
|
13 |
12
|
a1i |
|
14 |
|
ioossre |
|
15 |
14
|
a1i |
|
16 |
11 13 15
|
ixpssmapc |
|
17 |
16 5
|
sseldd |
|
18 |
6
|
a1i |
|
19 |
4
|
ffvelrnda |
|
20 |
5
|
adantr |
|
21 |
|
simpr |
|
22 |
|
fvixp2 |
|
23 |
20 21 22
|
syl2anc |
|
24 |
14 23
|
sselid |
|
25 |
19 24
|
resubcld |
|
26 |
3
|
ffvelrnda |
|
27 |
26
|
rexrd |
|
28 |
19
|
rexrd |
|
29 |
|
iooltub |
|
30 |
27 28 23 29
|
syl3anc |
|
31 |
24 19
|
posdifd |
|
32 |
30 31
|
mpbid |
|
33 |
25 32
|
elrpd |
|
34 |
24 26
|
resubcld |
|
35 |
|
ioogtlb |
|
36 |
27 28 23 35
|
syl3anc |
|
37 |
26 24
|
posdifd |
|
38 |
36 37
|
mpbid |
|
39 |
34 38
|
elrpd |
|
40 |
33 39
|
ifcld |
|
41 |
40
|
ralrimiva |
|
42 |
|
eqid |
|
43 |
42
|
rnmptss |
|
44 |
41 43
|
syl |
|
45 |
18 44
|
eqsstrd |
|
46 |
|
ltso |
|
47 |
46
|
a1i |
|
48 |
42
|
rnmptfi |
|
49 |
1 48
|
syl |
|
50 |
6 49
|
eqeltrid |
|
51 |
11 40 42 2
|
rnmptn0 |
|
52 |
18 51
|
eqnetrd |
|
53 |
|
rpssre |
|
54 |
53
|
a1i |
|
55 |
45 54
|
sstrd |
|
56 |
|
fiinfcl |
|
57 |
47 50 52 55 56
|
syl13anc |
|
58 |
45 57
|
sseldd |
|
59 |
7 58
|
eqeltrid |
|
60 |
|
rpxr |
|
61 |
59 60
|
syl |
|
62 |
|
eqid |
|
63 |
62
|
blopn |
|
64 |
10 17 61 63
|
syl3anc |
|
65 |
8
|
a1i |
|
66 |
1
|
rrxtopnfi |
|
67 |
9
|
eqcomi |
|
68 |
67
|
a1i |
|
69 |
68
|
fveq2d |
|
70 |
66 69
|
eqtrd |
|
71 |
65 70
|
eleq12d |
|
72 |
64 71
|
mpbird |
|
73 |
|
xmetpsmet |
|
74 |
10 73
|
syl |
|
75 |
|
blcntrps |
|
76 |
74 17 59 75
|
syl3anc |
|
77 |
65
|
eqcomd |
|
78 |
76 77
|
eleqtrd |
|
79 |
|
nfv |
|
80 |
|
elmapfn |
|
81 |
80
|
3ad2ant2 |
|
82 |
27
|
3ad2antl1 |
|
83 |
28
|
3ad2antl1 |
|
84 |
|
simpl2 |
|
85 |
|
simpr |
|
86 |
|
elmapi |
|
87 |
86
|
adantr |
|
88 |
|
simpr |
|
89 |
87 88
|
ffvelrnd |
|
90 |
84 85 89
|
syl2anc |
|
91 |
26
|
3ad2antl1 |
|
92 |
53 59
|
sselid |
|
93 |
92
|
adantr |
|
94 |
24 93
|
resubcld |
|
95 |
94
|
3ad2antl1 |
|
96 |
53 40
|
sselid |
|
97 |
7
|
a1i |
|
98 |
|
infxrrefi |
|
99 |
55 50 52 98
|
syl3anc |
|
100 |
99
|
eqcomd |
|
101 |
97 100
|
eqtrd |
|
102 |
101
|
adantr |
|
103 |
|
ressxr |
|
104 |
103
|
a1i |
|
105 |
55 104
|
sstrd |
|
106 |
105
|
adantr |
|
107 |
40
|
elexd |
|
108 |
42
|
elrnmpt1 |
|
109 |
21 107 108
|
syl2anc |
|
110 |
109 6
|
eleqtrrdi |
|
111 |
|
infxrlb |
|
112 |
106 110 111
|
syl2anc |
|
113 |
102 112
|
eqbrtrd |
|
114 |
|
min2 |
|
115 |
25 34 114
|
syl2anc |
|
116 |
93 96 34 113 115
|
letrd |
|
117 |
93 24 26 116
|
lesubd |
|
118 |
117
|
3ad2antl1 |
|
119 |
24
|
adantlr |
|
120 |
89
|
adantll |
|
121 |
119 120
|
resubcld |
|
122 |
121
|
3adantl3 |
|
123 |
1 9
|
rrndsmet |
|
124 |
123
|
ad2antrr |
|
125 |
17
|
ad2antrr |
|
126 |
|
simplr |
|
127 |
|
metcl |
|
128 |
124 125 126 127
|
syl3anc |
|
129 |
128
|
3adantl3 |
|
130 |
93
|
adantlr |
|
131 |
130
|
3adantl3 |
|
132 |
121
|
recnd |
|
133 |
132
|
abscld |
|
134 |
121
|
leabsd |
|
135 |
1
|
ad2antrr |
|
136 |
|
ixpf |
|
137 |
5 136
|
syl |
|
138 |
15
|
ralrimiva |
|
139 |
|
iunss |
|
140 |
138 139
|
sylibr |
|
141 |
137 140
|
fssd |
|
142 |
141
|
ad2antrr |
|
143 |
126 86
|
syl |
|
144 |
|
simpr |
|
145 |
|
eqid |
|
146 |
135 142 143 144 145
|
rrnprjdstle |
|
147 |
|
eqid |
|
148 |
|
eqid |
|
149 |
147 148
|
rrxdsfi |
|
150 |
1 149
|
syl |
|
151 |
150 68
|
eqtrd |
|
152 |
151
|
oveqd |
|
153 |
152
|
ad2antrr |
|
154 |
146 153
|
breqtrd |
|
155 |
121 133 128 134 154
|
letrd |
|
156 |
155
|
3adantl3 |
|
157 |
|
simpl3 |
|
158 |
122 129 131 156 157
|
lelttrd |
|
159 |
|
ltsub23 |
|
160 |
119 120 130 159
|
syl3anc |
|
161 |
160
|
3adantl3 |
|
162 |
158 161
|
mpbid |
|
163 |
91 95 90 118 162
|
lelttrd |
|
164 |
24 93
|
readdcld |
|
165 |
164
|
3ad2antl1 |
|
166 |
19
|
3ad2antl1 |
|
167 |
120 119
|
resubcld |
|
168 |
167
|
3adantl3 |
|
169 |
167
|
leabsd |
|
170 |
120
|
recnd |
|
171 |
119
|
recnd |
|
172 |
170 171
|
abssubd |
|
173 |
169 172
|
breqtrd |
|
174 |
167 133 128 173 154
|
letrd |
|
175 |
174
|
3adantl3 |
|
176 |
168 129 131 175 157
|
lelttrd |
|
177 |
119
|
3adantl3 |
|
178 |
90 177 131
|
ltsubadd2d |
|
179 |
176 178
|
mpbid |
|
180 |
|
min1 |
|
181 |
25 34 180
|
syl2anc |
|
182 |
93 96 25 113 181
|
letrd |
|
183 |
24 93 19
|
leaddsub2d |
|
184 |
182 183
|
mpbird |
|
185 |
184
|
3ad2antl1 |
|
186 |
90 165 166 179 185
|
ltletrd |
|
187 |
82 83 90 163 186
|
eliood |
|
188 |
187
|
ralrimiva |
|
189 |
81 188
|
jca |
|
190 |
|
vex |
|
191 |
190
|
elixp |
|
192 |
189 191
|
sylibr |
|
193 |
79 74 17 61 192
|
ballss3 |
|
194 |
65 193
|
eqsstrd |
|
195 |
78 194
|
jca |
|
196 |
|
eleq2 |
|
197 |
|
sseq1 |
|
198 |
196 197
|
anbi12d |
|
199 |
198
|
rspcev |
|
200 |
72 195 199
|
syl2anc |
|