Step |
Hyp |
Ref |
Expression |
1 |
|
mirval.p |
|
2 |
|
mirval.d |
|
3 |
|
mirval.i |
|
4 |
|
mirval.l |
|
5 |
|
mirval.s |
|
6 |
|
mirval.g |
|
7 |
|
krippen.m |
|
8 |
|
krippen.n |
|
9 |
|
krippen.a |
|
10 |
|
krippen.b |
|
11 |
|
krippen.c |
|
12 |
|
krippen.e |
|
13 |
|
krippen.f |
|
14 |
|
krippen.x |
|
15 |
|
krippen.y |
|
16 |
|
krippen.1 |
|
17 |
|
krippen.2 |
|
18 |
|
krippen.3 |
|
19 |
|
krippen.4 |
|
20 |
|
krippen.5 |
|
21 |
|
krippen.6 |
|
22 |
|
krippen.l |
|
23 |
|
krippen.7 |
|
24 |
16
|
adantr |
|
25 |
6
|
adantr |
|
26 |
11
|
adantr |
|
27 |
9
|
adantr |
|
28 |
10
|
adantr |
|
29 |
18
|
adantr |
|
30 |
23
|
adantr |
|
31 |
|
simpr |
|
32 |
31
|
oveq2d |
|
33 |
30 32
|
breqtrd |
|
34 |
1 2 3 22 25 26 27 26 28 33
|
legeq |
|
35 |
1 2 3 25 26 27 26 28 29 34
|
tgcgreq |
|
36 |
20
|
adantr |
|
37 |
35 34 36
|
3eqtr3rd |
|
38 |
14
|
adantr |
|
39 |
1 2 3 4 5 25 38 7 27
|
mirinv |
|
40 |
37 39
|
mpbid |
|
41 |
13
|
adantr |
|
42 |
19
|
adantr |
|
43 |
42 32
|
eqtr3d |
|
44 |
1 2 3 25 26 41 26 43
|
axtgcgrid |
|
45 |
21
|
adantr |
|
46 |
31 44 45
|
3eqtrrd |
|
47 |
15
|
adantr |
|
48 |
12
|
adantr |
|
49 |
1 2 3 4 5 25 47 8 48
|
mirinv |
|
50 |
46 49
|
mpbid |
|
51 |
40 50
|
oveq12d |
|
52 |
24 51
|
eleqtrrd |
|
53 |
6
|
adantr |
|
54 |
53
|
ad2antrr |
|
55 |
11
|
adantr |
|
56 |
|
eqid |
|
57 |
1 2 3 4 5 53 55 56
|
mirf |
|
58 |
15
|
adantr |
|
59 |
57 58
|
ffvelrnd |
|
60 |
59
|
ad2antrr |
|
61 |
|
simplr |
|
62 |
55
|
ad2antrr |
|
63 |
58
|
ad2antrr |
|
64 |
|
simprl |
|
65 |
1 2 3 4 5 6 11 56 15
|
mirbtwn |
|
66 |
65
|
ad3antrrr |
|
67 |
1 2 3 54 60 61 62 63 64 66
|
tgbtwnexch3 |
|
68 |
14
|
ad3antrrr |
|
69 |
9
|
adantr |
|
70 |
69
|
ad2antrr |
|
71 |
10
|
adantr |
|
72 |
71
|
ad2antrr |
|
73 |
|
eqid |
|
74 |
12
|
adantr |
|
75 |
57 74
|
ffvelrnd |
|
76 |
13
|
adantr |
|
77 |
57 76
|
ffvelrnd |
|
78 |
6
|
ad2antrr |
|
79 |
9
|
ad2antrr |
|
80 |
75
|
adantr |
|
81 |
1 2 3 78 79 80
|
tgbtwntriv1 |
|
82 |
|
simpr |
|
83 |
82
|
oveq1d |
|
84 |
81 83
|
eleqtrd |
|
85 |
6
|
ad2antrr |
|
86 |
9
|
ad2antrr |
|
87 |
75
|
adantr |
|
88 |
11
|
ad2antrr |
|
89 |
12
|
ad2antrr |
|
90 |
|
simplr |
|
91 |
1 2 3 6 9 11 12 16
|
tgbtwncom |
|
92 |
91
|
ad2antrr |
|
93 |
1 2 3 4 5 85 88 56 89
|
mirbtwn |
|
94 |
1 2 3 85 87 88 89 93
|
tgbtwncom |
|
95 |
1 3 85 89 88 86 87 90 92 94
|
tgbtwnconn2 |
|
96 |
23
|
adantr |
|
97 |
1 2 3 4 5 53 55 56 74
|
mircgr |
|
98 |
96 97
|
breqtrrd |
|
99 |
98
|
adantr |
|
100 |
1 2 3 22 85 86 87 88 86 95 99
|
legbtwn |
|
101 |
84 100
|
pm2.61dane |
|
102 |
1 2 3 53 55 69 75 101
|
tgbtwncom |
|
103 |
6
|
ad2antrr |
|
104 |
10
|
ad2antrr |
|
105 |
77
|
adantr |
|
106 |
1 2 3 103 104 105
|
tgbtwntriv1 |
|
107 |
|
simpr |
|
108 |
107
|
oveq1d |
|
109 |
106 108
|
eleqtrd |
|
110 |
6
|
ad2antrr |
|
111 |
10
|
ad2antrr |
|
112 |
77
|
adantr |
|
113 |
11
|
ad2antrr |
|
114 |
13
|
ad2antrr |
|
115 |
6
|
adantr |
|
116 |
11
|
adantr |
|
117 |
12
|
adantr |
|
118 |
19
|
adantr |
|
119 |
|
simpr |
|
120 |
119
|
oveq2d |
|
121 |
118 120
|
eqtrd |
|
122 |
1 2 3 115 116 117 116 121
|
axtgcgrid |
|
123 |
122
|
eqcomd |
|
124 |
123
|
adantlr |
|
125 |
|
simplr |
|
126 |
125
|
neneqd |
|
127 |
124 126
|
pm2.65da |
|
128 |
127
|
neqned |
|
129 |
128
|
adantr |
|
130 |
1 2 3 6 10 11 13 17
|
tgbtwncom |
|
131 |
130
|
ad2antrr |
|
132 |
1 2 3 4 5 110 113 56 114
|
mirbtwn |
|
133 |
1 2 3 110 112 113 114 132
|
tgbtwncom |
|
134 |
1 3 110 114 113 111 112 129 131 133
|
tgbtwnconn2 |
|
135 |
23 18 19
|
3brtr3d |
|
136 |
135
|
adantr |
|
137 |
1 2 3 4 5 53 55 56 76
|
mircgr |
|
138 |
136 137
|
breqtrrd |
|
139 |
138
|
adantr |
|
140 |
1 2 3 22 110 111 112 113 111 134 139
|
legbtwn |
|
141 |
109 140
|
pm2.61dane |
|
142 |
1 2 3 53 55 71 77 141
|
tgbtwncom |
|
143 |
19
|
adantr |
|
144 |
143 97 137
|
3eqtr4d |
|
145 |
1 2 3 53 55 75 55 77 144
|
tgcgrcomlr |
|
146 |
18
|
adantr |
|
147 |
1 2 3 53 55 69 55 71 146
|
tgcgrcomlr |
|
148 |
|
eqid |
|
149 |
1 2 3 4 5 53 59 148 75
|
mircgr |
|
150 |
|
eqid |
|
151 |
|
eqid |
|
152 |
|
eqid |
|
153 |
21
|
adantr |
|
154 |
8
|
fveq1i |
|
155 |
153 154
|
eqtr2di |
|
156 |
1 2 3 4 5 53 56 150 151 152 55 58 74 76 155
|
mirauto |
|
157 |
156
|
oveq2d |
|
158 |
149 157
|
eqtr3d |
|
159 |
1 2 3 53 59 75 59 77 158
|
tgcgrcomlr |
|
160 |
|
eqidd |
|
161 |
1 2 3 53 75 69 55 59 77 71 55 59 102 142 145 147 159 160
|
tgifscgr |
|
162 |
1 2 3 53 69 59 71 59 161
|
tgcgrcomlr |
|
163 |
162
|
ad3antrrr |
|
164 |
54
|
adantr |
|
165 |
60
|
adantr |
|
166 |
61
|
adantr |
|
167 |
64
|
adantr |
|
168 |
|
simpr |
|
169 |
168
|
oveq2d |
|
170 |
167 169
|
eleqtrrd |
|
171 |
1 2 3 164 165 166 170
|
axtgbtwnid |
|
172 |
171
|
oveq1d |
|
173 |
171
|
oveq1d |
|
174 |
163 172 173
|
3eqtr3d |
|
175 |
53
|
ad3antrrr |
|
176 |
59
|
ad3antrrr |
|
177 |
55
|
ad3antrrr |
|
178 |
61
|
adantr |
|
179 |
|
eqid |
|
180 |
69
|
ad3antrrr |
|
181 |
71
|
ad3antrrr |
|
182 |
|
simpr |
|
183 |
60
|
adantr |
|
184 |
64
|
adantr |
|
185 |
1 4 3 175 183 178 177 184
|
btwncolg3 |
|
186 |
162
|
ad3antrrr |
|
187 |
146
|
ad3antrrr |
|
188 |
1 4 3 175 176 177 178 179 180 181 2 182 185 186 187
|
lncgr |
|
189 |
174 188
|
pm2.61dane |
|
190 |
189
|
eqcomd |
|
191 |
|
simprr |
|
192 |
1 2 3 54 70 61 72 191
|
tgbtwncom |
|
193 |
1 2 3 4 5 54 61 73 70 72 190 192
|
ismir |
|
194 |
193
|
eqcomd |
|
195 |
20
|
ad3antrrr |
|
196 |
7
|
fveq1i |
|
197 |
195 196
|
eqtr2di |
|
198 |
1 2 3 4 5 54 61 68 70 72 194 197
|
miduniq |
|
199 |
198
|
oveq1d |
|
200 |
67 199
|
eleqtrd |
|
201 |
1 2 3 4 5 53 58 8 74
|
mirbtwn |
|
202 |
153
|
oveq1d |
|
203 |
201 202
|
eleqtrrd |
|
204 |
1 2 3 53 76 58 74 203
|
tgbtwncom |
|
205 |
1 2 3 4 5 53 55 56 74 58 76 204
|
mirbtwni |
|
206 |
1 2 3 53 75 69 55 77 71 59 102 142 205
|
tgtrisegint |
|
207 |
200 206
|
r19.29a |
|
208 |
52 207
|
pm2.61dane |
|