Step |
Hyp |
Ref |
Expression |
1 |
|
frgr3v.v |
|
2 |
|
frgr3v.e |
|
3 |
1 2
|
isfrgr |
|
4 |
3
|
a1i |
|
5 |
|
id |
|
6 |
|
difeq1 |
|
7 |
|
reueq1 |
|
8 |
6 7
|
raleqbidv |
|
9 |
5 8
|
raleqbidv |
|
10 |
9
|
anbi2d |
|
11 |
10
|
baibd |
|
12 |
11
|
adantl |
|
13 |
4 12
|
bitrd |
|
14 |
|
sneq |
|
15 |
14
|
difeq2d |
|
16 |
|
preq2 |
|
17 |
16
|
preq1d |
|
18 |
17
|
sseq1d |
|
19 |
18
|
reubidv |
|
20 |
15 19
|
raleqbidv |
|
21 |
|
sneq |
|
22 |
21
|
difeq2d |
|
23 |
|
preq2 |
|
24 |
23
|
preq1d |
|
25 |
24
|
sseq1d |
|
26 |
25
|
reubidv |
|
27 |
22 26
|
raleqbidv |
|
28 |
|
sneq |
|
29 |
28
|
difeq2d |
|
30 |
|
preq2 |
|
31 |
30
|
preq1d |
|
32 |
31
|
sseq1d |
|
33 |
32
|
reubidv |
|
34 |
29 33
|
raleqbidv |
|
35 |
20 27 34
|
raltpg |
|
36 |
35
|
ad2antrr |
|
37 |
|
tprot |
|
38 |
37
|
a1i |
|
39 |
38
|
difeq1d |
|
40 |
|
necom |
|
41 |
40
|
biimpi |
|
42 |
|
necom |
|
43 |
42
|
biimpi |
|
44 |
41 43
|
anim12i |
|
45 |
44
|
3adant3 |
|
46 |
|
diftpsn3 |
|
47 |
45 46
|
syl |
|
48 |
39 47
|
eqtrd |
|
49 |
48
|
raleqdv |
|
50 |
|
tprot |
|
51 |
50
|
eqcomi |
|
52 |
51
|
a1i |
|
53 |
52
|
difeq1d |
|
54 |
|
id |
|
55 |
|
necom |
|
56 |
55
|
biimpi |
|
57 |
54 56
|
anim12ci |
|
58 |
57
|
3adant2 |
|
59 |
|
diftpsn3 |
|
60 |
58 59
|
syl |
|
61 |
53 60
|
eqtrd |
|
62 |
61
|
raleqdv |
|
63 |
|
diftpsn3 |
|
64 |
63
|
3adant1 |
|
65 |
64
|
raleqdv |
|
66 |
49 62 65
|
3anbi123d |
|
67 |
66
|
ad2antlr |
|
68 |
|
preq2 |
|
69 |
68
|
preq2d |
|
70 |
69
|
sseq1d |
|
71 |
70
|
reubidv |
|
72 |
|
preq2 |
|
73 |
72
|
preq2d |
|
74 |
73
|
sseq1d |
|
75 |
74
|
reubidv |
|
76 |
71 75
|
ralprg |
|
77 |
76
|
3adant1 |
|
78 |
72
|
preq2d |
|
79 |
78
|
sseq1d |
|
80 |
79
|
reubidv |
|
81 |
|
preq2 |
|
82 |
81
|
preq2d |
|
83 |
82
|
sseq1d |
|
84 |
83
|
reubidv |
|
85 |
80 84
|
ralprg |
|
86 |
85
|
ancoms |
|
87 |
86
|
3adant2 |
|
88 |
81
|
preq2d |
|
89 |
88
|
sseq1d |
|
90 |
89
|
reubidv |
|
91 |
68
|
preq2d |
|
92 |
91
|
sseq1d |
|
93 |
92
|
reubidv |
|
94 |
90 93
|
ralprg |
|
95 |
94
|
3adant3 |
|
96 |
77 87 95
|
3anbi123d |
|
97 |
96
|
ad2antrr |
|
98 |
36 67 97
|
3bitrd |
|
99 |
1 2
|
frgr3vlem2 |
|
100 |
99
|
imp |
|
101 |
|
simpll1 |
|
102 |
|
simpll3 |
|
103 |
|
simpll2 |
|
104 |
101 102 103
|
3jca |
|
105 |
|
simplr2 |
|
106 |
|
simplr1 |
|
107 |
58
|
simpld |
|
108 |
107
|
ad2antlr |
|
109 |
105 106 108
|
3jca |
|
110 |
|
tpcomb |
|
111 |
5 110
|
eqtrdi |
|
112 |
111
|
anim1i |
|
113 |
112
|
adantl |
|
114 |
|
reueq1 |
|
115 |
110 114
|
mp1i |
|
116 |
1 2
|
frgr3vlem2 |
|
117 |
116
|
imp |
|
118 |
115 117
|
bitrd |
|
119 |
104 109 113 118
|
syl21anc |
|
120 |
100 119
|
anbi12d |
|
121 |
103 102 101
|
3jca |
|
122 |
|
simplr3 |
|
123 |
106
|
necomd |
|
124 |
105
|
necomd |
|
125 |
122 123 124
|
3jca |
|
126 |
37
|
eqeq2i |
|
127 |
126
|
biimpi |
|
128 |
127
|
anim1i |
|
129 |
128
|
adantl |
|
130 |
|
reueq1 |
|
131 |
37 130
|
mp1i |
|
132 |
1 2
|
frgr3vlem2 |
|
133 |
132
|
imp |
|
134 |
131 133
|
bitrd |
|
135 |
121 125 129 134
|
syl21anc |
|
136 |
103 101 102
|
3jca |
|
137 |
123 122 105
|
3jca |
|
138 |
|
tpcoma |
|
139 |
138
|
eqeq2i |
|
140 |
139
|
biimpi |
|
141 |
140
|
anim1i |
|
142 |
141
|
adantl |
|
143 |
|
reueq1 |
|
144 |
138 143
|
mp1i |
|
145 |
1 2
|
frgr3vlem2 |
|
146 |
145
|
imp |
|
147 |
144 146
|
bitrd |
|
148 |
136 137 142 147
|
syl21anc |
|
149 |
135 148
|
anbi12d |
|
150 |
102 101 103
|
3jca |
|
151 |
124 108 106
|
3jca |
|
152 |
51
|
eqeq2i |
|
153 |
152
|
biimpi |
|
154 |
153
|
anim1i |
|
155 |
154
|
adantl |
|
156 |
|
reueq1 |
|
157 |
51 156
|
mp1i |
|
158 |
1 2
|
frgr3vlem2 |
|
159 |
158
|
imp |
|
160 |
157 159
|
bitrd |
|
161 |
150 151 155 160
|
syl21anc |
|
162 |
|
3anrev |
|
163 |
162
|
biimpi |
|
164 |
55 42 40
|
3anbi123i |
|
165 |
164
|
biimpi |
|
166 |
165
|
3com13 |
|
167 |
163 166
|
anim12i |
|
168 |
|
tpcoma |
|
169 |
37 168
|
eqtri |
|
170 |
169
|
eqeq2i |
|
171 |
170
|
biimpi |
|
172 |
171
|
anim1i |
|
173 |
|
reueq1 |
|
174 |
169 173
|
mp1i |
|
175 |
1 2
|
frgr3vlem2 |
|
176 |
175
|
imp |
|
177 |
174 176
|
bitrd |
|
178 |
167 172 177
|
syl2an |
|
179 |
161 178
|
anbi12d |
|
180 |
120 149 179
|
3anbi123d |
|
181 |
|
prcom |
|
182 |
181
|
eleq1i |
|
183 |
182
|
anbi2i |
|
184 |
183
|
anbi2i |
|
185 |
|
anandir |
|
186 |
184 185
|
bitr4i |
|
187 |
|
prcom |
|
188 |
187
|
eleq1i |
|
189 |
188
|
anbi2i |
|
190 |
189
|
anbi2i |
|
191 |
|
anandir |
|
192 |
190 191
|
bitr4i |
|
193 |
|
prcom |
|
194 |
193
|
eleq1i |
|
195 |
194
|
anbi2i |
|
196 |
195
|
anbi2i |
|
197 |
|
anandir |
|
198 |
196 197
|
bitr4i |
|
199 |
186 192 198
|
3anbi123i |
|
200 |
|
3anrot |
|
201 |
|
df-3an |
|
202 |
|
prcom |
|
203 |
202
|
eleq1i |
|
204 |
|
prcom |
|
205 |
204
|
eleq1i |
|
206 |
|
biid |
|
207 |
203 205 206
|
3anbi123i |
|
208 |
200 201 207
|
3bitr3i |
|
209 |
|
df-3an |
|
210 |
|
biid |
|
211 |
|
prcom |
|
212 |
211
|
eleq1i |
|
213 |
210 205 212
|
3anbi123i |
|
214 |
209 213
|
bitr3i |
|
215 |
|
df-3an |
|
216 |
|
3anrot |
|
217 |
|
3anrot |
|
218 |
|
biid |
|
219 |
203 218 212
|
3anbi123i |
|
220 |
216 217 219
|
3bitri |
|
221 |
215 220
|
bitr3i |
|
222 |
208 214 221
|
3anbi123i |
|
223 |
|
df-3an |
|
224 |
|
anabs1 |
|
225 |
|
anidm |
|
226 |
223 224 225
|
3bitri |
|
227 |
199 222 226
|
3bitri |
|
228 |
180 227
|
syl6bb |
|
229 |
13 98 228
|
3bitrd |
|
230 |
229
|
ex |
|