Step |
Hyp |
Ref |
Expression |
1 |
|
colperpex.p |
|
2 |
|
colperpex.d |
|
3 |
|
colperpex.i |
|
4 |
|
colperpex.l |
|
5 |
|
colperpex.g |
|
6 |
|
mideu.s |
|
7 |
|
mideu.1 |
|
8 |
|
mideu.2 |
|
9 |
|
mideulem.1 |
|
10 |
|
mideulem.2 |
|
11 |
|
mideulem.3 |
|
12 |
|
mideulem.4 |
|
13 |
|
mideulem.5 |
|
14 |
|
mideulem.6 |
|
15 |
|
mideulem.7 |
|
16 |
|
mideulem.8 |
|
17 |
|
opphllem.1 |
|
18 |
|
opphllem.2 |
|
19 |
|
opphllem.3 |
|
20 |
5
|
adantr |
|
21 |
|
eqid |
|
22 |
8
|
adantr |
|
23 |
11
|
adantr |
|
24 |
7
|
adantr |
|
25 |
17
|
adantr |
|
26 |
|
simprl |
|
27 |
9
|
necomd |
|
28 |
27
|
neneqd |
|
29 |
28
|
adantr |
|
30 |
4 5 14
|
perpln2 |
|
31 |
1 3 4 5 7 11 30
|
tglnne |
|
32 |
31
|
necomd |
|
33 |
32
|
neneqd |
|
34 |
33
|
adantr |
|
35 |
29 34
|
jca |
|
36 |
5
|
adantr |
|
37 |
8
|
adantr |
|
38 |
7
|
adantr |
|
39 |
11
|
adantr |
|
40 |
1 3 4 5 8 7 27
|
tglinerflx2 |
|
41 |
1 3 4 5 7 8 9
|
tglinecom |
|
42 |
41 14
|
eqbrtrrd |
|
43 |
1 2 3 4 5 8 7 40 11 42
|
perprag |
|
44 |
43
|
adantr |
|
45 |
|
simpr |
|
46 |
45
|
orcd |
|
47 |
1 2 3 4 6 36 37 38 39 44 46
|
ragflat3 |
|
48 |
|
oran |
|
49 |
47 48
|
sylib |
|
50 |
35 49
|
pm2.65da |
|
51 |
50
|
adantr |
|
52 |
41
|
adantr |
|
53 |
51 52
|
neleqtrrd |
|
54 |
9
|
adantr |
|
55 |
54
|
neneqd |
|
56 |
53 55
|
jca |
|
57 |
|
pm4.56 |
|
58 |
56 57
|
sylib |
|
59 |
1 4 3 20 24 22 23 58
|
ncolrot2 |
|
60 |
|
simprrr |
|
61 |
1 2 3 20 25 26 23 60
|
tgbtwncom |
|
62 |
12
|
adantr |
|
63 |
15
|
adantr |
|
64 |
|
simprrl |
|
65 |
1 3 4 20 62 24 22 26 63 64
|
coltr3 |
|
66 |
50 41
|
neleqtrrd |
|
67 |
66
|
adantr |
|
68 |
|
nelne2 |
|
69 |
65 67 68
|
syl2anc |
|
70 |
1 2 3 20 23 26 25 61 69
|
tgbtwnne |
|
71 |
1 2 3 4 6 5 8 7 11
|
israg |
|
72 |
43 71
|
mpbid |
|
73 |
72
|
ad3antrrr |
|
74 |
5
|
ad3antrrr |
|
75 |
|
eqid |
|
76 |
1 2 3 4 6 20 24 75 23
|
mircl |
|
77 |
76
|
ad2antrr |
|
78 |
7
|
ad3antrrr |
|
79 |
11
|
ad3antrrr |
|
80 |
17
|
ad3antrrr |
|
81 |
8
|
ad3antrrr |
|
82 |
|
simplr |
|
83 |
1 2 3 4 6 74 78 75 79
|
mirbtwn |
|
84 |
|
eqid |
|
85 |
1 2 3 4 6 74 81 84 82
|
mirbtwn |
|
86 |
|
simpr |
|
87 |
74
|
ad2antrr |
|
88 |
78
|
ad2antrr |
|
89 |
81
|
ad2antrr |
|
90 |
54
|
ad4antr |
|
91 |
10
|
ad5antr |
|
92 |
79
|
ad2antrr |
|
93 |
62
|
ad4antr |
|
94 |
13
|
ad5antr |
|
95 |
14
|
ad5antr |
|
96 |
63
|
ad4antr |
|
97 |
16
|
ad5antr |
|
98 |
80
|
ad2antrr |
|
99 |
18
|
ad5antr |
|
100 |
19
|
ad5antr |
|
101 |
26
|
ad2antrr |
|
102 |
101
|
ad2antrr |
|
103 |
|
simp-5r |
|
104 |
103
|
simprd |
|
105 |
104
|
simpld |
|
106 |
104
|
simprd |
|
107 |
82
|
ad2antrr |
|
108 |
|
simpllr |
|
109 |
108
|
simpld |
|
110 |
|
simprr |
|
111 |
110
|
ad2antrr |
|
112 |
|
simplr |
|
113 |
1 2 3 4 87 6 88 89 90 91 92 93 94 95 96 97 98 99 100 102 105 106 107 109 111 112 86
|
mideulem2 |
|
114 |
113
|
eqcomd |
|
115 |
114
|
fveq2d |
|
116 |
115
|
fveq1d |
|
117 |
86 116
|
eqtrd |
|
118 |
|
eqid |
|
119 |
1 2 3 4 6 74 118 82 80 101 110
|
midexlem |
|
120 |
117 119
|
r19.29a |
|
121 |
120
|
oveq1d |
|
122 |
85 121
|
eleqtrrd |
|
123 |
1 2 3 4 6 74 78 75 79
|
mircgr |
|
124 |
19
|
ad3antrrr |
|
125 |
123 124
|
eqtrd |
|
126 |
1 2 3 74 78 77 81 80 125
|
tgcgrcomlr |
|
127 |
120
|
oveq2d |
|
128 |
1 2 3 4 6 74 81 84 82
|
mircgr |
|
129 |
124 127 128
|
3eqtrd |
|
130 |
1 2 3 74 77 78 79 80 81 82 83 122 126 129
|
tgcgrextend |
|
131 |
1 2 3 74 77 80
|
axtgcgrrflx |
|
132 |
1 2 3 74 79 80
|
axtgcgrrflx |
|
133 |
60
|
ad2antrr |
|
134 |
|
simprl |
|
135 |
1 2 3 74 77 101 82 134
|
tgbtwncom |
|
136 |
1 2 3 74 101 82 101 80 110
|
tgcgrcomlr |
|
137 |
136
|
eqcomd |
|
138 |
43
|
ad3antrrr |
|
139 |
54
|
necomd |
|
140 |
139
|
ad2antrr |
|
141 |
65
|
ad2antrr |
|
142 |
141
|
orcd |
|
143 |
1 4 3 74 78 81 101 142
|
colcom |
|
144 |
1 4 3 74 81 78 101 143
|
colrot1 |
|
145 |
1 2 3 4 6 74 81 78 79 101 138 140 144
|
ragcol |
|
146 |
1 2 3 4 6 74 101 78 79
|
israg |
|
147 |
145 146
|
mpbid |
|
148 |
1 2 3 74 80 101 79 82 101 77 133 135 137 147
|
tgcgrextend |
|
149 |
132 148
|
eqtrd |
|
150 |
1 2 3 74 77 78 79 80 80 81 82 77 83 122 130 129 131 149
|
tgifscgr |
|
151 |
73 150
|
eqtr4d |
|
152 |
1 2 3 20 76 26 26 25
|
axtgsegcon |
|
153 |
151 152
|
r19.29a |
|
154 |
19
|
adantr |
|
155 |
1 2 3 20 24 23 22 25 154
|
tgcgrcomlr |
|
156 |
143 152
|
r19.29a |
|
157 |
1 4 3 20 23 25 26 61
|
btwncolg1 |
|
158 |
1 2 3 4 6 20 21 22 23 24 25 26 59 70 153 155 156 157
|
symquadlem |
|
159 |
1 2 3 4 6 20 26 21 24
|
mirbtwn |
|
160 |
158
|
oveq1d |
|
161 |
159 160
|
eleqtrrd |
|
162 |
1 2 3 20 22 26 24 161
|
tgbtwncom |
|
163 |
1 2 3 20 24 22
|
axtgcgrrflx |
|
164 |
158
|
oveq2d |
|
165 |
1 2 3 4 6 20 26 21 24
|
mircgr |
|
166 |
164 165
|
eqtrd |
|
167 |
1 2 3 20 24 26 22 23 22 26 24 25 162 161 163 166 154 153
|
tgifscgr |
|
168 |
1 2 3 4 6 20 26 21 25 23 167 61
|
ismir |
|
169 |
158 168
|
jca |
|
170 |
1 2 3 5 10 12 11 16
|
tgbtwncom |
|
171 |
1 2 3 5 11 8 10 12 17 170 18
|
axtgpasch |
|
172 |
169 171
|
reximddv |
|