Step |
Hyp |
Ref |
Expression |
1 |
|
colperpex.p |
|
2 |
|
colperpex.d |
|
3 |
|
colperpex.i |
|
4 |
|
colperpex.l |
|
5 |
|
colperpex.g |
|
6 |
|
colperpex.1 |
|
7 |
|
colperpex.2 |
|
8 |
|
colperpex.3 |
|
9 |
|
colperpex.4 |
|
10 |
|
colperpexlem3.1 |
|
11 |
|
eqid |
|
12 |
5
|
ad2antrr |
|
13 |
|
eqid |
|
14 |
1 3 4 5 6 7 9
|
tgelrnln |
|
15 |
14
|
ad2antrr |
|
16 |
|
simplr |
|
17 |
1 4 3 12 15 16
|
tglnpt |
|
18 |
|
eqid |
|
19 |
8
|
ad2antrr |
|
20 |
1 2 3 4 11 12 17 18 19
|
mircl |
|
21 |
6
|
ad2antrr |
|
22 |
|
eqid |
|
23 |
1 2 3 4 11 12 21 22 19
|
mircl |
|
24 |
1 2 3 4 11 12 21 22 19
|
mircgr |
|
25 |
7
|
ad2antrr |
|
26 |
10
|
ad2antrr |
|
27 |
|
nelne2 |
|
28 |
16 26 27
|
syl2anc |
|
29 |
1 3 4 12 17 19 28
|
tgelrnln |
|
30 |
1 3 4 12 17 19 28
|
tglinecom |
|
31 |
|
simpr |
|
32 |
30 31
|
eqbrtrd |
|
33 |
1 2 3 4 12 29 15 32
|
perpcom |
|
34 |
1 2 3 4 12 21 25 16 19 33
|
perprag |
|
35 |
1 2 3 4 11 12 21 17 19
|
israg |
|
36 |
34 35
|
mpbid |
|
37 |
24 36
|
eqtr2d |
|
38 |
1 2 3 4 11 12 13 20 23 21 37
|
midexlem |
|
39 |
12
|
ad2antrr |
|
40 |
23
|
ad2antrr |
|
41 |
21
|
ad2antrr |
|
42 |
19
|
ad2antrr |
|
43 |
20
|
ad2antrr |
|
44 |
17
|
ad2antrr |
|
45 |
|
simplr |
|
46 |
1 2 3 4 11 39 41 22 42
|
mirbtwn |
|
47 |
1 2 3 4 11 39 44 18 42
|
mirbtwn |
|
48 |
1 2 3 4 11 39 45 13 43
|
mirbtwn |
|
49 |
|
simpr |
|
50 |
49
|
eqcomd |
|
51 |
50
|
oveq1d |
|
52 |
48 51
|
eleqtrd |
|
53 |
1 2 3 39 40 41 42 43 44 45 46 47 52
|
tgtrisegint |
|
54 |
39
|
ad3antrrr |
|
55 |
41
|
ad3antrrr |
|
56 |
|
simpllr |
|
57 |
|
simplrr |
|
58 |
|
simpr |
|
59 |
58
|
oveq2d |
|
60 |
57 59
|
eleqtrd |
|
61 |
1 2 3 54 55 56 60
|
axtgbtwnid |
|
62 |
61
|
eqcomd |
|
63 |
62
|
oveq1d |
|
64 |
50
|
ad3antrrr |
|
65 |
58
|
fveq2d |
|
66 |
65
|
fveq1d |
|
67 |
64 66
|
eqtr4d |
|
68 |
45
|
ad3antrrr |
|
69 |
43
|
ad3antrrr |
|
70 |
1 2 3 4 11 54 68 13 69
|
mirinv |
|
71 |
67 70
|
mpbid |
|
72 |
44
|
ad3antrrr |
|
73 |
58
|
oveq1d |
|
74 |
57 73
|
eleqtrrd |
|
75 |
1 2 3 54 72 56 74
|
axtgbtwnid |
|
76 |
75
|
eqcomd |
|
77 |
71 76
|
oveq12d |
|
78 |
34
|
ad2antrr |
|
79 |
1 2 3 4 11 39 45 13 43 50
|
mircom |
|
80 |
28
|
ad2antrr |
|
81 |
1 2 3 4 39 11 22 18 13 41 44 42 45 78 79 80
|
colperpexlem2 |
|
82 |
81
|
ad3antrrr |
|
83 |
62 82
|
eqnetrd |
|
84 |
1 3 4 54 56 68 83
|
tglinecom |
|
85 |
42
|
ad3antrrr |
|
86 |
80
|
ad3antrrr |
|
87 |
54
|
adantr |
|
88 |
72
|
adantr |
|
89 |
85
|
adantr |
|
90 |
1 2 3 4 11 87 88 18
|
mircinv |
|
91 |
|
simpr |
|
92 |
90 91
|
eqtr4d |
|
93 |
1 2 3 4 11 87 88 18 88 89 92
|
mireq |
|
94 |
86
|
adantr |
|
95 |
94
|
neneqd |
|
96 |
93 95
|
pm2.65da |
|
97 |
96
|
neqned |
|
98 |
47
|
ad3antrrr |
|
99 |
1 3 4 54 72 85 69 86 98
|
btwnlng2 |
|
100 |
1 3 4 54 72 85 86 69 97 99
|
tglineelsb2 |
|
101 |
28
|
necomd |
|
102 |
101
|
ad5antr |
|
103 |
1 3 4 54 85 72 102
|
tglinecom |
|
104 |
1 3 4 54 69 72 97
|
tglinecom |
|
105 |
100 103 104
|
3eqtr4d |
|
106 |
77 84 105
|
3eqtr4d |
|
107 |
63 106
|
eqtr3d |
|
108 |
31
|
ad5antr |
|
109 |
107 108
|
eqbrtrd |
|
110 |
39
|
ad3antrrr |
|
111 |
41
|
ad3antrrr |
|
112 |
45
|
ad3antrrr |
|
113 |
81
|
ad3antrrr |
|
114 |
1 3 4 110 111 112 113
|
tgelrnln |
|
115 |
15
|
ad5antr |
|
116 |
1 3 4 110 111 112 113
|
tglinerflx1 |
|
117 |
9
|
ad2antrr |
|
118 |
1 3 4 12 21 25 117
|
tglinerflx1 |
|
119 |
118
|
ad5antr |
|
120 |
116 119
|
elind |
|
121 |
1 3 4 110 111 112 113
|
tglinerflx2 |
|
122 |
16
|
ad5antr |
|
123 |
113
|
necomd |
|
124 |
|
simpr |
|
125 |
44
|
ad3antrrr |
|
126 |
1 2 3 4 39 11 22 18 13 41 44 42 45 78 79
|
colperpexlem1 |
|
127 |
126
|
ad3antrrr |
|
128 |
1 2 3 4 11 110 125 111 112 127
|
ragcom |
|
129 |
1 2 3 4 110 114 115 120 121 122 123 124 128
|
ragperp |
|
130 |
109 129
|
pm2.61dane |
|
131 |
118
|
ad5antr |
|
132 |
62 131
|
eqeltrd |
|
133 |
132
|
orcd |
|
134 |
25
|
ad5antr |
|
135 |
117
|
ad5antr |
|
136 |
|
simpllr |
|
137 |
124
|
necomd |
|
138 |
|
simplrr |
|
139 |
1 3 4 110 111 125 136 137 138
|
btwnlng1 |
|
140 |
1 3 4 110 111 134 135 125 124 122 136 139
|
tglineeltr |
|
141 |
140
|
orcd |
|
142 |
133 141
|
pm2.61dane |
|
143 |
39
|
ad2antrr |
|
144 |
45
|
ad2antrr |
|
145 |
|
simplr |
|
146 |
42
|
ad2antrr |
|
147 |
|
simprl |
|
148 |
1 2 3 143 144 145 146 147
|
tgbtwncom |
|
149 |
130 142 148
|
jca32 |
|
150 |
149
|
ex |
|
151 |
150
|
reximdva |
|
152 |
53 151
|
mpd |
|
153 |
|
r19.42v |
|
154 |
152 153
|
sylib |
|
155 |
154
|
ex |
|
156 |
155
|
reximdva |
|
157 |
38 156
|
mpd |
|
158 |
1 2 3 4 5 14 8 10
|
footex |
|
159 |
157 158
|
r19.29a |
|