Step |
Hyp |
Ref |
Expression |
1 |
|
ismid.p |
|
2 |
|
ismid.d |
|
3 |
|
ismid.i |
|
4 |
|
ismid.g |
|
5 |
|
ismid.1 |
|
6 |
|
lmieu.l |
|
7 |
|
lmieu.1 |
|
8 |
|
lmieu.a |
|
9 |
8
|
adantr |
|
10 |
|
simpr |
|
11 |
|
eqidd |
|
12 |
4
|
ad4antr |
|
13 |
5
|
ad4antr |
|
14 |
9
|
ad3antrrr |
|
15 |
|
simpllr |
|
16 |
|
eqid |
|
17 |
1 2 3 12 13 14 15
|
midcl |
|
18 |
1 2 3 12 13 14 15 16 17
|
ismidb |
|
19 |
11 18
|
mpbird |
|
20 |
19
|
adantr |
|
21 |
12
|
adantr |
|
22 |
7
|
ad4antr |
|
23 |
22
|
adantr |
|
24 |
14
|
adantr |
|
25 |
15
|
adantr |
|
26 |
10
|
neqned |
|
27 |
26
|
adantr |
|
28 |
1 3 6 21 24 25 27
|
tgelrnln |
|
29 |
|
simpr |
|
30 |
|
simp-4r |
|
31 |
30
|
adantr |
|
32 |
1 3 6 21 24 25 27
|
tglinerflx1 |
|
33 |
31 32
|
elind |
|
34 |
|
simpllr |
|
35 |
1 2 3 12 13 14 15
|
midbtwn |
|
36 |
1 3 6 12 14 15 17 26 35
|
btwnlng1 |
|
37 |
36
|
adantr |
|
38 |
34 37
|
elind |
|
39 |
1 3 6 21 23 28 29 33 38
|
tglineineq |
|
40 |
39
|
fveq2d |
|
41 |
40
|
fveq1d |
|
42 |
|
eqid |
|
43 |
1 2 3 6 16 21 24 42
|
mircinv |
|
44 |
20 41 43
|
3eqtr2rd |
|
45 |
10 44
|
mtand |
|
46 |
4
|
ad5antr |
|
47 |
7
|
ad5antr |
|
48 |
|
nne |
|
49 |
45 48
|
sylib |
|
50 |
49
|
adantr |
|
51 |
50 47
|
eqeltrrd |
|
52 |
|
simpr |
|
53 |
1 2 3 6 46 47 51 52
|
perpneq |
|
54 |
45 53
|
mtand |
|
55 |
54
|
ex |
|
56 |
55
|
con4d |
|
57 |
|
idd |
|
58 |
56 57
|
jaod |
|
59 |
58
|
impr |
|
60 |
59
|
eqcomd |
|
61 |
|
simpr |
|
62 |
61
|
oveq2d |
|
63 |
1 2 3 4 5 8 8
|
midid |
|
64 |
63
|
ad3antrrr |
|
65 |
62 64
|
eqtrd |
|
66 |
|
simpllr |
|
67 |
65 66
|
eqeltrd |
|
68 |
61
|
eqcomd |
|
69 |
68
|
olcd |
|
70 |
67 69
|
jca |
|
71 |
60 70
|
impbida |
|
72 |
71
|
ralrimiva |
|
73 |
|
reu6i |
|
74 |
9 72 73
|
syl2anc |
|
75 |
4
|
adantr |
|
76 |
75
|
ad2antrr |
|
77 |
7
|
adantr |
|
78 |
77
|
ad2antrr |
|
79 |
|
simplr |
|
80 |
1 6 3 76 78 79
|
tglnpt |
|
81 |
|
eqid |
|
82 |
8
|
adantr |
|
83 |
82
|
ad2antrr |
|
84 |
1 2 3 6 16 76 80 81 83
|
mircl |
|
85 |
|
oveq2 |
|
86 |
85
|
breq1d |
|
87 |
|
simprl |
|
88 |
|
simpr |
|
89 |
1 2 3 6 75 77 82 88
|
foot |
|
90 |
|
reurmo |
|
91 |
89 90
|
syl |
|
92 |
91
|
ad4antr |
|
93 |
79
|
ad2antrr |
|
94 |
|
simpllr |
|
95 |
76
|
ad2antrr |
|
96 |
83
|
ad2antrr |
|
97 |
|
simplr |
|
98 |
5
|
ad5antr |
|
99 |
1 2 3 95 98 96 97
|
midcl |
|
100 |
1 2 3 95 98 96 97
|
midbtwn |
|
101 |
88
|
ad4antr |
|
102 |
|
nelne2 |
|
103 |
87 101 102
|
syl2anc |
|
104 |
1 2 3 95 96 99 97 100 103
|
tgbtwnne |
|
105 |
1 3 6 95 96 97 99 104 100
|
btwnlng1 |
|
106 |
1 3 6 95 96 97 104 99 103 105
|
tglineelsb2 |
|
107 |
78
|
ad2antrr |
|
108 |
1 3 6 95 96 97 104
|
tgelrnln |
|
109 |
104
|
neneqd |
|
110 |
|
simprr |
|
111 |
110
|
orcomd |
|
112 |
111
|
ord |
|
113 |
109 112
|
mpd |
|
114 |
1 2 3 6 95 107 108 113
|
perpcom |
|
115 |
106 114
|
eqbrtrrd |
|
116 |
86 87 92 93 94 115
|
rmoi2 |
|
117 |
116
|
eqcomd |
|
118 |
80
|
ad2antrr |
|
119 |
1 2 3 95 98 96 97 16 118
|
ismidb |
|
120 |
117 119
|
mpbird |
|
121 |
|
simpr |
|
122 |
76
|
ad2antrr |
|
123 |
5
|
ad5antr |
|
124 |
83
|
ad2antrr |
|
125 |
|
simplr |
|
126 |
80
|
ad2antrr |
|
127 |
1 2 3 122 123 124 125 16 126
|
ismidb |
|
128 |
121 127
|
mpbid |
|
129 |
79
|
ad2antrr |
|
130 |
128 129
|
eqeltrd |
|
131 |
122
|
adantr |
|
132 |
|
simp-4r |
|
133 |
6 131 132
|
perpln1 |
|
134 |
78
|
ad3antrrr |
|
135 |
1 2 3 6 131 133 134 132
|
perpcom |
|
136 |
124
|
adantr |
|
137 |
126
|
adantr |
|
138 |
1 3 6 131 136 137 133
|
tglnne |
|
139 |
|
simpllr |
|
140 |
|
simpr |
|
141 |
140
|
necomd |
|
142 |
1 2 3 6 16 131 137 81 136
|
mirbtwn |
|
143 |
|
simplr |
|
144 |
143
|
oveq1d |
|
145 |
142 144
|
eleqtrrd |
|
146 |
1 3 6 131 139 136 137 141 145
|
btwnlng1 |
|
147 |
1 3 6 131 136 137 139 138 146 141
|
lnrot1 |
|
148 |
1 3 6 131 136 137 138 139 141 147
|
tglineelsb2 |
|
149 |
135 148
|
breqtrd |
|
150 |
149
|
ex |
|
151 |
150
|
necon1bd |
|
152 |
151
|
orrd |
|
153 |
130 152
|
jca |
|
154 |
120 153
|
impbida |
|
155 |
154
|
ralrimiva |
|
156 |
|
reu6i |
|
157 |
84 155 156
|
syl2anc |
|
158 |
1 2 3 6 75 77 82 88
|
footex |
|
159 |
157 158
|
r19.29a |
|
160 |
74 159
|
pm2.61dan |
|