Step |
Hyp |
Ref |
Expression |
1 |
|
ismid.p |
|
2 |
|
ismid.d |
|
3 |
|
ismid.i |
|
4 |
|
ismid.g |
|
5 |
|
ismid.1 |
|
6 |
|
lmif.m |
|
7 |
|
lmif.l |
|
8 |
|
lmif.d |
|
9 |
|
lmiiso.1 |
|
10 |
|
lmiiso.2 |
|
11 |
|
lmiisolem.s |
|
12 |
|
lmiisolem.z |
|
13 |
4
|
adantr |
|
14 |
1 2 3 4 5 6 7 8 9
|
lmicl |
|
15 |
1 2 3 4 5 9 14
|
midcl |
|
16 |
1 2 3 4 5 6 7 8 10
|
lmicl |
|
17 |
1 2 3 4 5 10 16
|
midcl |
|
18 |
1 2 3 4 5 15 17
|
midcl |
|
19 |
12 18
|
eqeltrid |
|
20 |
19
|
adantr |
|
21 |
|
eqid |
|
22 |
1 2 3 7 21 4 19 11 9
|
mircl |
|
23 |
22
|
adantr |
|
24 |
9
|
adantr |
|
25 |
1 2 3 7 21 13 20 11 24
|
mircgr |
|
26 |
|
simpr |
|
27 |
26
|
eqcomd |
|
28 |
1 2 3 13 20 23 20 24 25 27
|
tgcgreq |
|
29 |
|
simpr |
|
30 |
29
|
oveq2d |
|
31 |
12 30
|
eqtr4id |
|
32 |
4
|
adantr |
|
33 |
5
|
adantr |
|
34 |
15
|
adantr |
|
35 |
1 2 3 32 33 34 34
|
midid |
|
36 |
31 35
|
eqtrd |
|
37 |
|
eqidd |
|
38 |
1 2 3 4 5 6 7 8 9 14
|
islmib |
|
39 |
37 38
|
mpbid |
|
40 |
39
|
simpld |
|
41 |
40
|
adantr |
|
42 |
36 41
|
eqeltrd |
|
43 |
4
|
adantr |
|
44 |
15
|
adantr |
|
45 |
17
|
adantr |
|
46 |
19
|
adantr |
|
47 |
|
simpr |
|
48 |
1 2 3 4 5 15 17
|
midbtwn |
|
49 |
12 48
|
eqeltrid |
|
50 |
49
|
adantr |
|
51 |
1 3 7 43 44 45 46 47 50
|
btwnlng1 |
|
52 |
8
|
adantr |
|
53 |
40
|
adantr |
|
54 |
|
eqidd |
|
55 |
1 2 3 4 5 6 7 8 10 16
|
islmib |
|
56 |
54 55
|
mpbid |
|
57 |
56
|
simpld |
|
58 |
57
|
adantr |
|
59 |
1 3 7 43 44 45 47 47 52 53 58
|
tglinethru |
|
60 |
51 59
|
eleqtrrd |
|
61 |
42 60
|
pm2.61dane |
|
62 |
61
|
adantr |
|
63 |
28 62
|
eqeltrrd |
|
64 |
1 2 3 4 5 6 7 8 9
|
lmiinv |
|
65 |
64
|
biimpar |
|
66 |
63 65
|
syldan |
|
67 |
66 28
|
eqtr4d |
|
68 |
67
|
oveq1d |
|
69 |
|
eqidd |
|
70 |
4
|
adantr |
|
71 |
10
|
adantr |
|
72 |
17
|
adantr |
|
73 |
1 2 3 4 5 10 16
|
midbtwn |
|
74 |
73
|
adantr |
|
75 |
|
simpr |
|
76 |
75
|
oveq2d |
|
77 |
74 76
|
eleqtrrd |
|
78 |
1 2 3 70 71 72 77
|
axtgbtwnid |
|
79 |
|
eqidd |
|
80 |
69 78 79
|
s3eqd |
|
81 |
1 2 3 7 21 4 19 10 10
|
ragtrivb |
|
82 |
81
|
adantr |
|
83 |
80 82
|
eqeltrrd |
|
84 |
4
|
adantr |
|
85 |
61
|
adantr |
|
86 |
57
|
adantr |
|
87 |
10
|
adantr |
|
88 |
|
df-ne |
|
89 |
56
|
simprd |
|
90 |
89
|
orcomd |
|
91 |
90
|
orcanai |
|
92 |
88 91
|
sylan2b |
|
93 |
16
|
adantr |
|
94 |
|
simpr |
|
95 |
17
|
adantr |
|
96 |
4
|
adantr |
|
97 |
10
|
adantr |
|
98 |
16
|
adantr |
|
99 |
5
|
adantr |
|
100 |
|
simpr |
|
101 |
1 2 3 96 99 97 98 100
|
midcgr |
|
102 |
101
|
eqcomd |
|
103 |
1 2 3 96 97 98 97 102
|
axtgcgrid |
|
104 |
103
|
ex |
|
105 |
104
|
necon3d |
|
106 |
105
|
imp |
|
107 |
73
|
adantr |
|
108 |
1 3 7 84 87 93 95 94 107
|
btwnlng1 |
|
109 |
1 3 7 84 87 93 94 95 106 108
|
tglineelsb2 |
|
110 |
1 3 7 84 95 87 106
|
tglinecom |
|
111 |
109 110
|
eqtr4d |
|
112 |
92 111
|
breqtrd |
|
113 |
1 2 3 7 84 85 86 87 112
|
perpdrag |
|
114 |
83 113
|
pm2.61dane |
|
115 |
1 2 3 7 21 4 19 17 10
|
israg |
|
116 |
114 115
|
mpbid |
|
117 |
|
eqidd |
|
118 |
1 2 3 4 5 10 16 21 17
|
ismidb |
|
119 |
117 118
|
mpbird |
|
120 |
119
|
oveq2d |
|
121 |
116 120
|
eqtr4d |
|
122 |
121
|
adantr |
|
123 |
28
|
oveq1d |
|
124 |
68 122 123
|
3eqtr2d |
|
125 |
4
|
adantr |
|
126 |
22
|
adantr |
|
127 |
19
|
adantr |
|
128 |
9
|
adantr |
|
129 |
1 2 3 7 21 4 19 11 14
|
mircl |
|
130 |
129
|
adantr |
|
131 |
14
|
adantr |
|
132 |
10
|
adantr |
|
133 |
16
|
adantr |
|
134 |
|
simpr |
|
135 |
1 2 3 7 21 125 127 11 128
|
mirbtwn |
|
136 |
1 2 3 7 21 125 127 11 131
|
mirbtwn |
|
137 |
|
eqidd |
|
138 |
4
|
adantr |
|
139 |
9
|
adantr |
|
140 |
15
|
adantr |
|
141 |
1 2 3 4 5 9 14
|
midbtwn |
|
142 |
141
|
adantr |
|
143 |
|
simpr |
|
144 |
143
|
oveq2d |
|
145 |
142 144
|
eleqtrrd |
|
146 |
1 2 3 138 139 140 145
|
axtgbtwnid |
|
147 |
|
eqidd |
|
148 |
137 146 147
|
s3eqd |
|
149 |
1 2 3 7 21 4 19 9 9
|
ragtrivb |
|
150 |
149
|
adantr |
|
151 |
148 150
|
eqeltrrd |
|
152 |
4
|
adantr |
|
153 |
61
|
adantr |
|
154 |
40
|
adantr |
|
155 |
9
|
adantr |
|
156 |
|
df-ne |
|
157 |
39
|
simprd |
|
158 |
157
|
orcomd |
|
159 |
158
|
orcanai |
|
160 |
156 159
|
sylan2b |
|
161 |
14
|
adantr |
|
162 |
|
simpr |
|
163 |
15
|
adantr |
|
164 |
4
|
adantr |
|
165 |
9
|
adantr |
|
166 |
14
|
adantr |
|
167 |
5
|
adantr |
|
168 |
|
simpr |
|
169 |
1 2 3 164 167 165 166 168
|
midcgr |
|
170 |
169
|
eqcomd |
|
171 |
1 2 3 164 165 166 165 170
|
axtgcgrid |
|
172 |
171
|
ex |
|
173 |
172
|
necon3d |
|
174 |
173
|
imp |
|
175 |
141
|
adantr |
|
176 |
1 3 7 152 155 161 163 162 175
|
btwnlng1 |
|
177 |
1 3 7 152 155 161 162 163 174 176
|
tglineelsb2 |
|
178 |
1 3 7 152 163 155 174
|
tglinecom |
|
179 |
177 178
|
eqtr4d |
|
180 |
160 179
|
breqtrd |
|
181 |
1 2 3 7 152 153 154 155 180
|
perpdrag |
|
182 |
151 181
|
pm2.61dane |
|
183 |
1 2 3 7 21 4 19 15 9
|
israg |
|
184 |
182 183
|
mpbid |
|
185 |
|
eqidd |
|
186 |
1 2 3 4 5 9 14 21 15
|
ismidb |
|
187 |
185 186
|
mpbird |
|
188 |
187
|
oveq2d |
|
189 |
184 188
|
eqtr4d |
|
190 |
1 2 3 7 21 4 19 11 9
|
mircgr |
|
191 |
1 2 3 7 21 4 19 11 14
|
mircgr |
|
192 |
189 190 191
|
3eqtr4d |
|
193 |
192
|
adantr |
|
194 |
1 2 3 125 127 126 127 130 193
|
tgcgrcomlr |
|
195 |
189
|
adantr |
|
196 |
11
|
fveq1i |
|
197 |
1 2 3 4 5 9 14 11 19
|
mirmid |
|
198 |
12
|
eqcomi |
|
199 |
1 2 3 4 5 15 17 21 19
|
ismidb |
|
200 |
198 199
|
mpbiri |
|
201 |
196 197 200
|
3eqtr4a |
|
202 |
1 2 3 4 5 22 129 21 17
|
ismidb |
|
203 |
201 202
|
mpbird |
|
204 |
119 203
|
oveq12d |
|
205 |
|
eqid |
|
206 |
1 2 3 7 21 4 17 205 10 22
|
miriso |
|
207 |
204 206
|
eqtr2d |
|
208 |
207
|
adantr |
|
209 |
1 2 3 125 132 126 133 130 208
|
tgcgrcomlr |
|
210 |
121
|
adantr |
|
211 |
1 2 3 125 126 127 128 130 127 131 132 133 134 135 136 194 195 209 210
|
axtg5seg |
|
212 |
211
|
eqcomd |
|
213 |
124 212
|
pm2.61dane |
|