Step |
Hyp |
Ref |
Expression |
1 |
|
qustgp.h |
|
2 |
|
qustgpopn.x |
|
3 |
|
qustgpopn.j |
|
4 |
|
qustgpopn.k |
|
5 |
|
qustgpopn.f |
|
6 |
|
qustgplem.m |
|
7 |
1
|
qusgrp |
|
8 |
7
|
adantl |
|
9 |
1
|
a1i |
|
10 |
2
|
a1i |
|
11 |
|
ovex |
|
12 |
11
|
a1i |
|
13 |
|
simpl |
|
14 |
9 10 5 12 13
|
qusval |
|
15 |
9 10 5 12 13
|
quslem |
|
16 |
14 10 15 13 3 4
|
imastopn |
|
17 |
3 2
|
tgptopon |
|
18 |
17
|
adantr |
|
19 |
|
qtoptopon |
|
20 |
18 15 19
|
syl2anc |
|
21 |
16 20
|
eqeltrd |
|
22 |
9 10 12 13
|
qusbas |
|
23 |
22
|
fveq2d |
|
24 |
21 23
|
eleqtrd |
|
25 |
|
eqid |
|
26 |
25 4
|
istps |
|
27 |
24 26
|
sylibr |
|
28 |
|
eqid |
|
29 |
25 28
|
grpsubf |
|
30 |
8 29
|
syl |
|
31 |
|
cnvimass |
|
32 |
30
|
fdmd |
|
33 |
32
|
adantr |
|
34 |
31 33
|
sseqtrid |
|
35 |
|
relxp |
|
36 |
|
relss |
|
37 |
34 35 36
|
mpisyl |
|
38 |
34
|
sseld |
|
39 |
|
vex |
|
40 |
39
|
elqs |
|
41 |
22
|
adantr |
|
42 |
41
|
eleq2d |
|
43 |
40 42
|
bitr3id |
|
44 |
|
vex |
|
45 |
44
|
elqs |
|
46 |
41
|
eleq2d |
|
47 |
45 46
|
bitr3id |
|
48 |
43 47
|
anbi12d |
|
49 |
|
reeanv |
|
50 |
|
opelxp |
|
51 |
48 49 50
|
3bitr4g |
|
52 |
8
|
ad2antrr |
|
53 |
52 29
|
syl |
|
54 |
|
ffn |
|
55 |
|
elpreima |
|
56 |
53 54 55
|
3syl |
|
57 |
|
df-ov |
|
58 |
|
simpllr |
|
59 |
|
simprl |
|
60 |
|
simprr |
|
61 |
|
eqid |
|
62 |
1 2 61 28
|
qussub |
|
63 |
58 59 60 62
|
syl3anc |
|
64 |
57 63
|
syl5eqr |
|
65 |
64
|
eleq1d |
|
66 |
|
simpr |
|
67 |
|
tgpgrp |
|
68 |
67
|
adantr |
|
69 |
2 61
|
grpsubf |
|
70 |
|
ffn |
|
71 |
68 69 70
|
3syl |
|
72 |
|
fnov |
|
73 |
71 72
|
sylib |
|
74 |
3 61
|
tgpsubcn |
|
75 |
74
|
adantr |
|
76 |
73 75
|
eqeltrrd |
|
77 |
|
ecexg |
|
78 |
11 77
|
ax-mp |
|
79 |
78 5
|
fnmpti |
|
80 |
|
qtopid |
|
81 |
18 79 80
|
sylancl |
|
82 |
16
|
oveq2d |
|
83 |
81 82
|
eleqtrrd |
|
84 |
5 83
|
eqeltrrid |
|
85 |
|
eceq1 |
|
86 |
18 18 76 18 84 85
|
cnmpt21 |
|
87 |
6 86
|
eqeltrid |
|
88 |
87
|
ad2antrr |
|
89 |
|
simplr |
|
90 |
|
cnima |
|
91 |
88 89 90
|
syl2anc |
|
92 |
18
|
ad2antrr |
|
93 |
|
eltx |
|
94 |
92 92 93
|
syl2anc |
|
95 |
91 94
|
mpbid |
|
96 |
|
ecexg |
|
97 |
11 96
|
ax-mp |
|
98 |
6 97
|
fnmpoi |
|
99 |
|
elpreima |
|
100 |
98 99
|
ax-mp |
|
101 |
|
opelxp |
|
102 |
101
|
anbi1i |
|
103 |
|
df-ov |
|
104 |
|
oveq12 |
|
105 |
104
|
eceq1d |
|
106 |
|
ecexg |
|
107 |
11 106
|
ax-mp |
|
108 |
105 6 107
|
ovmpoa |
|
109 |
103 108
|
syl5eqr |
|
110 |
109
|
eleq1d |
|
111 |
110
|
pm5.32i |
|
112 |
100 102 111
|
3bitri |
|
113 |
|
eleq1 |
|
114 |
|
opelxp |
|
115 |
113 114
|
bitrdi |
|
116 |
115
|
anbi1d |
|
117 |
116
|
2rexbidv |
|
118 |
117
|
rspccv |
|
119 |
112 118
|
syl5bir |
|
120 |
95 119
|
syl |
|
121 |
66 120
|
mpand |
|
122 |
|
simp-4l |
|
123 |
58
|
adantr |
|
124 |
|
simprll |
|
125 |
1 2 3 4 5
|
qustgpopn |
|
126 |
122 123 124 125
|
syl3anc |
|
127 |
|
simprlr |
|
128 |
1 2 3 4 5
|
qustgpopn |
|
129 |
122 123 127 128
|
syl3anc |
|
130 |
59
|
adantr |
|
131 |
|
eceq1 |
|
132 |
131 5 78
|
fvmpt3i |
|
133 |
130 132
|
syl |
|
134 |
122 17
|
syl |
|
135 |
|
toponss |
|
136 |
134 124 135
|
syl2anc |
|
137 |
|
simprrl |
|
138 |
137
|
simpld |
|
139 |
|
fnfvima |
|
140 |
79 136 138 139
|
mp3an2i |
|
141 |
133 140
|
eqeltrrd |
|
142 |
60
|
adantr |
|
143 |
|
eceq1 |
|
144 |
143 5 78
|
fvmpt3i |
|
145 |
142 144
|
syl |
|
146 |
|
toponss |
|
147 |
134 127 146
|
syl2anc |
|
148 |
137
|
simprd |
|
149 |
|
fnfvima |
|
150 |
79 147 148 149
|
mp3an2i |
|
151 |
145 150
|
eqeltrrd |
|
152 |
141 151
|
opelxpd |
|
153 |
136
|
sselda |
|
154 |
147
|
sselda |
|
155 |
153 154
|
anim12dan |
|
156 |
|
eceq1 |
|
157 |
156 5 78
|
fvmpt3i |
|
158 |
|
eceq1 |
|
159 |
158 5 78
|
fvmpt3i |
|
160 |
|
opeq12 |
|
161 |
157 159 160
|
syl2an |
|
162 |
155 161
|
syl |
|
163 |
123
|
adantr |
|
164 |
1 2 25
|
quseccl |
|
165 |
1 2 25
|
quseccl |
|
166 |
164 165
|
anim12dan |
|
167 |
163 155 166
|
syl2anc |
|
168 |
|
opelxpi |
|
169 |
167 168
|
syl |
|
170 |
1 2 61 28
|
qussub |
|
171 |
170
|
3expb |
|
172 |
163 155 171
|
syl2anc |
|
173 |
|
oveq12 |
|
174 |
173
|
eceq1d |
|
175 |
|
ecexg |
|
176 |
11 175
|
ax-mp |
|
177 |
174 6 176
|
ovmpoa |
|
178 |
155 177
|
syl |
|
179 |
172 178
|
eqtr4d |
|
180 |
|
df-ov |
|
181 |
|
df-ov |
|
182 |
179 180 181
|
3eqtr3g |
|
183 |
|
opelxpi |
|
184 |
|
simprrr |
|
185 |
184
|
sselda |
|
186 |
183 185
|
sylan2 |
|
187 |
|
elpreima |
|
188 |
98 187
|
ax-mp |
|
189 |
188
|
simprbi |
|
190 |
186 189
|
syl |
|
191 |
182 190
|
eqeltrd |
|
192 |
53 54
|
syl |
|
193 |
192
|
ad2antrr |
|
194 |
|
elpreima |
|
195 |
193 194
|
syl |
|
196 |
169 191 195
|
mpbir2and |
|
197 |
162 196
|
eqeltrd |
|
198 |
197
|
ralrimivva |
|
199 |
|
opeq1 |
|
200 |
199
|
eleq1d |
|
201 |
200
|
ralbidv |
|
202 |
201
|
ralima |
|
203 |
79 202
|
mpan |
|
204 |
|
opeq2 |
|
205 |
204
|
eleq1d |
|
206 |
205
|
ralima |
|
207 |
79 206
|
mpan |
|
208 |
207
|
ralbidv |
|
209 |
203 208
|
sylan9bb |
|
210 |
136 147 209
|
syl2anc |
|
211 |
198 210
|
mpbird |
|
212 |
|
dfss3 |
|
213 |
|
eleq1 |
|
214 |
213
|
ralxp |
|
215 |
212 214
|
bitri |
|
216 |
211 215
|
sylibr |
|
217 |
|
xpeq1 |
|
218 |
217
|
eleq2d |
|
219 |
217
|
sseq1d |
|
220 |
218 219
|
anbi12d |
|
221 |
|
xpeq2 |
|
222 |
221
|
eleq2d |
|
223 |
221
|
sseq1d |
|
224 |
222 223
|
anbi12d |
|
225 |
220 224
|
rspc2ev |
|
226 |
126 129 152 216 225
|
syl112anc |
|
227 |
226
|
expr |
|
228 |
227
|
rexlimdvva |
|
229 |
121 228
|
syld |
|
230 |
65 229
|
sylbid |
|
231 |
230
|
adantld |
|
232 |
56 231
|
sylbid |
|
233 |
|
opeq12 |
|
234 |
233
|
eleq1d |
|
235 |
233
|
eleq1d |
|
236 |
|
opex |
|
237 |
|
eleq1 |
|
238 |
237
|
anbi1d |
|
239 |
238
|
2rexbidv |
|
240 |
236 239
|
elab |
|
241 |
235 240
|
bitrdi |
|
242 |
234 241
|
imbi12d |
|
243 |
232 242
|
syl5ibrcom |
|
244 |
243
|
rexlimdvva |
|
245 |
51 244
|
sylbird |
|
246 |
245
|
com23 |
|
247 |
38 246
|
mpdd |
|
248 |
37 247
|
relssdv |
|
249 |
|
ssabral |
|
250 |
248 249
|
sylib |
|
251 |
|
eltx |
|
252 |
24 24 251
|
syl2anc |
|
253 |
252
|
adantr |
|
254 |
250 253
|
mpbird |
|
255 |
254
|
ralrimiva |
|
256 |
|
txtopon |
|
257 |
24 24 256
|
syl2anc |
|
258 |
|
iscn |
|
259 |
257 24 258
|
syl2anc |
|
260 |
30 255 259
|
mpbir2and |
|
261 |
4 28
|
istgp2 |
|
262 |
8 27 260 261
|
syl3anbrc |
|