Step |
Hyp |
Ref |
Expression |
1 |
|
cyc3genpm.t |
|
2 |
|
cyc3genpm.a |
|
3 |
|
cyc3genpm.s |
|
4 |
|
cyc3genpm.n |
|
5 |
|
cyc3genpm.m |
|
6 |
|
cyc3genpmlem.t |
|
7 |
|
cyc3genpmlem.i |
|
8 |
|
cyc3genpmlem.j |
|
9 |
|
cyc3genpmlem.k |
|
10 |
|
cyc3genpmlem.l |
|
11 |
|
cyc3genpmlem.e |
|
12 |
|
cyc3genpmlem.f |
|
13 |
|
cyc3genpmlem.d |
|
14 |
|
cyc3genpmlem.1 |
|
15 |
|
cyc3genpmlem.2 |
|
16 |
|
wrd0 |
|
17 |
16
|
a1i |
|
18 |
|
simpr |
|
19 |
18
|
oveq2d |
|
20 |
19
|
eqeq2d |
|
21 |
5 13 7 8 14 3
|
cycpm2cl |
|
22 |
11 21
|
eqeltrd |
|
23 |
5 13 9 10 15 3
|
cycpm2cl |
|
24 |
12 23
|
eqeltrd |
|
25 |
|
eqid |
|
26 |
3 25 6
|
symgov |
|
27 |
22 24 26
|
syl2anc |
|
28 |
27
|
ad2antrr |
|
29 |
11
|
ad2antrr |
|
30 |
|
eqid |
|
31 |
5 13 7 8 14 30
|
cycpm2tr |
|
32 |
31
|
ad2antrr |
|
33 |
29 32
|
eqtrd |
|
34 |
5 13 9 10 15 30
|
cycpm2tr |
|
35 |
34
|
ad2antrr |
|
36 |
12
|
ad2antrr |
|
37 |
7
|
ad2antrr |
|
38 |
8
|
ad2antrr |
|
39 |
14
|
ad2antrr |
|
40 |
|
simplr |
|
41 |
|
simpr |
|
42 |
40 41
|
prssd |
|
43 |
|
ssprsseq |
|
44 |
43
|
biimpa |
|
45 |
37 38 39 42 44
|
syl31anc |
|
46 |
45
|
fveq2d |
|
47 |
35 36 46
|
3eqtr4d |
|
48 |
33 47
|
coeq12d |
|
49 |
13
|
ad2antrr |
|
50 |
37 38
|
prssd |
|
51 |
|
pr2nelem |
|
52 |
37 38 39 51
|
syl3anc |
|
53 |
|
eqid |
|
54 |
30 53
|
pmtrrn |
|
55 |
49 50 52 54
|
syl3anc |
|
56 |
30 53
|
pmtrfinv |
|
57 |
55 56
|
syl |
|
58 |
28 48 57
|
3eqtrd |
|
59 |
3
|
symgid |
|
60 |
49 59
|
syl |
|
61 |
|
eqid |
|
62 |
61
|
gsum0 |
|
63 |
60 62
|
eqtr4di |
|
64 |
58 63
|
eqtrd |
|
65 |
17 20 64
|
rspcedvd |
|
66 |
13
|
ad2antrr |
|
67 |
7
|
ad2antrr |
|
68 |
9 10
|
prssd |
|
69 |
68
|
ad2antrr |
|
70 |
|
simplr |
|
71 |
|
pr2nelem |
|
72 |
9 10 15 71
|
syl3anc |
|
73 |
72
|
ad2antrr |
|
74 |
|
unidifsnel |
|
75 |
70 73 74
|
syl2anc |
|
76 |
69 75
|
sseldd |
|
77 |
8
|
ad2antrr |
|
78 |
|
unidifsnne |
|
79 |
70 73 78
|
syl2anc |
|
80 |
79
|
necomd |
|
81 |
|
nelne2 |
|
82 |
75 81
|
sylancom |
|
83 |
14
|
necomd |
|
84 |
83
|
ad2antrr |
|
85 |
5 3 66 67 76 77 80 82 84
|
cycpm3cl2 |
|
86 |
85 1
|
eleqtrrdi |
|
87 |
86
|
s1cld |
|
88 |
|
simpr |
|
89 |
88
|
oveq2d |
|
90 |
89
|
eqeq2d |
|
91 |
5 3 66 67 76 77 80 82 84 6
|
cyc3co2 |
|
92 |
5 3 66 67 76 77 80 82 84
|
cycpm3cl |
|
93 |
25
|
gsumws1 |
|
94 |
92 93
|
syl |
|
95 |
11
|
ad2antrr |
|
96 |
|
en2eleq |
|
97 |
70 73 96
|
syl2anc |
|
98 |
97
|
fveq2d |
|
99 |
12 34
|
eqtrd |
|
100 |
99
|
ad2antrr |
|
101 |
5 66 67 76 80 30
|
cycpm2tr |
|
102 |
98 100 101
|
3eqtr4d |
|
103 |
95 102
|
oveq12d |
|
104 |
91 94 103
|
3eqtr4rd |
|
105 |
87 90 104
|
rspcedvd |
|
106 |
65 105
|
pm2.61dan |
|
107 |
13
|
ad2antrr |
|
108 |
8
|
ad2antrr |
|
109 |
68
|
ad2antrr |
|
110 |
|
simpr |
|
111 |
72
|
ad2antrr |
|
112 |
|
unidifsnel |
|
113 |
110 111 112
|
syl2anc |
|
114 |
109 113
|
sseldd |
|
115 |
7
|
ad2antrr |
|
116 |
|
unidifsnne |
|
117 |
110 111 116
|
syl2anc |
|
118 |
117
|
necomd |
|
119 |
|
simplr |
|
120 |
|
nelne2 |
|
121 |
113 119 120
|
syl2anc |
|
122 |
14
|
ad2antrr |
|
123 |
5 3 107 108 114 115 118 121 122
|
cycpm3cl2 |
|
124 |
123 1
|
eleqtrrdi |
|
125 |
124
|
s1cld |
|
126 |
|
simpr |
|
127 |
126
|
oveq2d |
|
128 |
127
|
eqeq2d |
|
129 |
5 3 107 108 114 115 118 121 122 6
|
cyc3co2 |
|
130 |
5 3 107 108 114 115 118 121 122
|
cycpm3cl |
|
131 |
25
|
gsumws1 |
|
132 |
130 131
|
syl |
|
133 |
|
prcom |
|
134 |
133
|
fveq2i |
|
135 |
5 13 8 7 83 30
|
cycpm2tr |
|
136 |
134 31 135
|
3eqtr4a |
|
137 |
11 136
|
eqtrd |
|
138 |
137
|
ad2antrr |
|
139 |
|
en2eleq |
|
140 |
110 111 139
|
syl2anc |
|
141 |
140
|
fveq2d |
|
142 |
99
|
ad2antrr |
|
143 |
5 107 108 114 118 30
|
cycpm2tr |
|
144 |
141 142 143
|
3eqtr4d |
|
145 |
138 144
|
oveq12d |
|
146 |
129 132 145
|
3eqtr4rd |
|
147 |
125 128 146
|
rspcedvd |
|
148 |
13
|
ad2antrr |
|
149 |
8
|
ad2antrr |
|
150 |
9
|
ad2antrr |
|
151 |
7
|
ad2antrr |
|
152 |
|
simpr |
|
153 |
149 152
|
nelpr1 |
|
154 |
|
prid1g |
|
155 |
9 154
|
syl |
|
156 |
155
|
ad2antrr |
|
157 |
|
simplr |
|
158 |
|
nelne2 |
|
159 |
156 157 158
|
syl2anc |
|
160 |
14
|
ad2antrr |
|
161 |
5 3 148 149 150 151 153 159 160
|
cycpm3cl2 |
|
162 |
161 1
|
eleqtrrdi |
|
163 |
10
|
ad2antrr |
|
164 |
15
|
ad2antrr |
|
165 |
|
prid2g |
|
166 |
163 165
|
syl |
|
167 |
|
nelne2 |
|
168 |
166 167
|
sylancom |
|
169 |
5 3 148 150 163 149 164 168 153
|
cycpm3cl2 |
|
170 |
169 1
|
eleqtrrdi |
|
171 |
162 170
|
s2cld |
|
172 |
|
simpr |
|
173 |
172
|
oveq2d |
|
174 |
173
|
eqeq2d |
|
175 |
148 59
|
syl |
|
176 |
175
|
oveq1d |
|
177 |
3
|
symggrp |
|
178 |
13 177
|
syl |
|
179 |
178
|
ad2antrr |
|
180 |
23
|
ad2antrr |
|
181 |
25 6 61
|
grplid |
|
182 |
179 180 181
|
syl2anc |
|
183 |
176 182
|
eqtrd |
|
184 |
183
|
oveq2d |
|
185 |
21
|
ad2antrr |
|
186 |
5 148 149 150 153 30
|
cycpm2tr |
|
187 |
53 3 25
|
symgtrf |
|
188 |
8 9
|
prssd |
|
189 |
188
|
ad2antrr |
|
190 |
|
pr2nelem |
|
191 |
149 150 153 190
|
syl3anc |
|
192 |
30 53
|
pmtrrn |
|
193 |
148 189 191 192
|
syl3anc |
|
194 |
187 193
|
sseldi |
|
195 |
186 194
|
eqeltrd |
|
196 |
153
|
necomd |
|
197 |
5 148 150 149 196 30
|
cycpm2tr |
|
198 |
|
prcom |
|
199 |
198
|
a1i |
|
200 |
199
|
fveq2d |
|
201 |
197 200
|
eqtr4d |
|
202 |
201 194
|
eqeltrd |
|
203 |
25 6
|
grpcl |
|
204 |
179 202 180 203
|
syl3anc |
|
205 |
25 6
|
grpass |
|
206 |
179 185 195 204 205
|
syl13anc |
|
207 |
25 6
|
grpass |
|
208 |
179 195 202 180 207
|
syl13anc |
|
209 |
208
|
oveq2d |
|
210 |
186 201
|
oveq12d |
|
211 |
3 25 6
|
symgov |
|
212 |
194 194 211
|
syl2anc |
|
213 |
30 53
|
pmtrfinv |
|
214 |
193 213
|
syl |
|
215 |
210 212 214
|
3eqtrd |
|
216 |
215
|
oveq1d |
|
217 |
216
|
oveq2d |
|
218 |
206 209 217
|
3eqtr2rd |
|
219 |
184 218
|
eqtr3d |
|
220 |
11 12
|
oveq12d |
|
221 |
220
|
ad2antrr |
|
222 |
5 3 148 149 150 151 153 159 160 6
|
cyc3co2 |
|
223 |
136
|
oveq1d |
|
224 |
223
|
ad2antrr |
|
225 |
222 224
|
eqtr4d |
|
226 |
5 3 148 150 163 149 164 168 153 6
|
cyc3co2 |
|
227 |
225 226
|
oveq12d |
|
228 |
219 221 227
|
3eqtr4d |
|
229 |
178
|
grpmndd |
|
230 |
229
|
ad2antrr |
|
231 |
5 3 148 149 150 151 153 159 160
|
cycpm3cl |
|
232 |
226 204
|
eqeltrd |
|
233 |
25 6
|
gsumws2 |
|
234 |
230 231 232 233
|
syl3anc |
|
235 |
228 234
|
eqtr4d |
|
236 |
171 174 235
|
rspcedvd |
|
237 |
147 236
|
pm2.61dan |
|
238 |
106 237
|
pm2.61dan |
|