Step |
Hyp |
Ref |
Expression |
1 |
|
mbfresfi.1 |
|
2 |
|
mbfresfi.2 |
|
3 |
|
mbfresfi.3 |
|
4 |
|
mbfresfi.4 |
|
5 |
2
|
uniexd |
|
6 |
4 5
|
eqeltrrd |
|
7 |
|
fex |
|
8 |
7
|
ex |
|
9 |
1 8
|
syl |
|
10 |
6 9
|
jcai |
|
11 |
|
feq2 |
|
12 |
11
|
anbi1d |
|
13 |
|
eqeq2 |
|
14 |
12 13
|
anbi12d |
|
15 |
14
|
imbi1d |
|
16 |
15
|
imbi2d |
|
17 |
|
feq1 |
|
18 |
|
reseq1 |
|
19 |
18
|
eleq1d |
|
20 |
19
|
ralbidv |
|
21 |
17 20
|
anbi12d |
|
22 |
21
|
anbi1d |
|
23 |
|
eleq1 |
|
24 |
22 23
|
imbi12d |
|
25 |
24
|
imbi2d |
|
26 |
|
rzal |
|
27 |
26
|
biantrud |
|
28 |
27
|
bicomd |
|
29 |
|
unieq |
|
30 |
|
uni0 |
|
31 |
29 30
|
eqtrdi |
|
32 |
31
|
eqeq1d |
|
33 |
28 32
|
anbi12d |
|
34 |
33
|
imbi1d |
|
35 |
34
|
2albidv |
|
36 |
|
raleq |
|
37 |
36
|
anbi2d |
|
38 |
|
unieq |
|
39 |
38
|
eqeq1d |
|
40 |
37 39
|
anbi12d |
|
41 |
40
|
imbi1d |
|
42 |
41
|
2albidv |
|
43 |
|
simpl |
|
44 |
|
simpr |
|
45 |
43 44
|
feq12d |
|
46 |
|
reseq1 |
|
47 |
46
|
adantr |
|
48 |
47
|
eleq1d |
|
49 |
48
|
ralbidv |
|
50 |
45 49
|
anbi12d |
|
51 |
|
eqeq2 |
|
52 |
51
|
adantl |
|
53 |
50 52
|
anbi12d |
|
54 |
|
eleq1 |
|
55 |
54
|
adantr |
|
56 |
53 55
|
imbi12d |
|
57 |
56
|
cbval2vw |
|
58 |
42 57
|
syl6bb |
|
59 |
|
raleq |
|
60 |
59
|
anbi2d |
|
61 |
|
unieq |
|
62 |
61
|
eqeq1d |
|
63 |
60 62
|
anbi12d |
|
64 |
63
|
imbi1d |
|
65 |
64
|
2albidv |
|
66 |
|
raleq |
|
67 |
66
|
anbi2d |
|
68 |
|
unieq |
|
69 |
68
|
eqeq1d |
|
70 |
67 69
|
anbi12d |
|
71 |
70
|
imbi1d |
|
72 |
71
|
2albidv |
|
73 |
|
frel |
|
74 |
73
|
adantr |
|
75 |
|
fdm |
|
76 |
|
eqcom |
|
77 |
76
|
biimpi |
|
78 |
75 77
|
sylan9eq |
|
79 |
|
reldm0 |
|
80 |
79
|
biimpar |
|
81 |
|
mbf0 |
|
82 |
80 81
|
eqeltrdi |
|
83 |
74 78 82
|
syl2anc |
|
84 |
83
|
gen2 |
|
85 |
|
ref |
|
86 |
|
fco |
|
87 |
85 86
|
mpan |
|
88 |
87
|
adantr |
|
89 |
88
|
ad2antrl |
|
90 |
|
recncf |
|
91 |
90
|
elexi |
|
92 |
|
vex |
|
93 |
91 92
|
coex |
|
94 |
93
|
resex |
|
95 |
|
vuniex |
|
96 |
|
eqcom |
|
97 |
96
|
biimpi |
|
98 |
97
|
adantl |
|
99 |
98
|
biantrud |
|
100 |
|
eqid |
|
101 |
|
feq123 |
|
102 |
100 101
|
mp3an3 |
|
103 |
|
reseq1 |
|
104 |
103
|
eleq1d |
|
105 |
104
|
adantr |
|
106 |
105
|
ralbidv |
|
107 |
102 106
|
anbi12d |
|
108 |
99 107
|
bitr3d |
|
109 |
|
eleq1 |
|
110 |
109
|
adantr |
|
111 |
108 110
|
imbi12d |
|
112 |
111
|
spc2gv |
|
113 |
94 95 112
|
mp2an |
|
114 |
|
ax-resscn |
|
115 |
|
fss |
|
116 |
85 114 115
|
mp2an |
|
117 |
|
fco |
|
118 |
116 117
|
mpan |
|
119 |
|
ssun1 |
|
120 |
119
|
unissi |
|
121 |
|
id |
|
122 |
120 121
|
sseqtrid |
|
123 |
|
fssres |
|
124 |
118 122 123
|
syl2an |
|
125 |
124
|
adantlr |
|
126 |
|
elssuni |
|
127 |
126
|
resabs1d |
|
128 |
|
resco |
|
129 |
127 128
|
eqtrdi |
|
130 |
129
|
adantl |
|
131 |
|
elun1 |
|
132 |
|
reseq2 |
|
133 |
132
|
eleq1d |
|
134 |
133
|
rspccva |
|
135 |
131 134
|
sylan2 |
|
136 |
135
|
adantll |
|
137 |
|
fresin |
|
138 |
|
ismbfcn |
|
139 |
137 138
|
syl |
|
140 |
139
|
biimpd |
|
141 |
140
|
ad2antrr |
|
142 |
136 141
|
mpd |
|
143 |
142
|
simpld |
|
144 |
130 143
|
eqeltrd |
|
145 |
144
|
ralrimiva |
|
146 |
|
reseq2 |
|
147 |
146
|
eleq1d |
|
148 |
147
|
cbvralvw |
|
149 |
145 148
|
sylib |
|
150 |
149
|
adantr |
|
151 |
|
pm2.27 |
|
152 |
125 150 151
|
syl2anc |
|
153 |
113 152
|
mpan9 |
|
154 |
|
vsnid |
|
155 |
|
elun2 |
|
156 |
|
reseq2 |
|
157 |
156
|
eleq1d |
|
158 |
157
|
rspcv |
|
159 |
154 155 158
|
mp2b |
|
160 |
|
resco |
|
161 |
|
fresin |
|
162 |
|
ismbfcn |
|
163 |
161 162
|
syl |
|
164 |
163
|
simprbda |
|
165 |
160 164
|
eqeltrid |
|
166 |
159 165
|
sylan2 |
|
167 |
166
|
ad2antrl |
|
168 |
|
uniun |
|
169 |
|
vex |
|
170 |
169
|
unisn |
|
171 |
170
|
uneq2i |
|
172 |
168 171
|
eqtri |
|
173 |
172 121
|
syl5eqr |
|
174 |
173
|
ad2antll |
|
175 |
89 153 167 174
|
mbfres2 |
|
176 |
|
imf |
|
177 |
|
fco |
|
178 |
176 177
|
mpan |
|
179 |
178
|
adantr |
|
180 |
179
|
ad2antrl |
|
181 |
|
imcncf |
|
182 |
181
|
elexi |
|
183 |
182 92
|
coex |
|
184 |
183
|
resex |
|
185 |
97
|
adantl |
|
186 |
185
|
biantrud |
|
187 |
|
feq123 |
|
188 |
100 187
|
mp3an3 |
|
189 |
|
reseq1 |
|
190 |
189
|
eleq1d |
|
191 |
190
|
adantr |
|
192 |
191
|
ralbidv |
|
193 |
188 192
|
anbi12d |
|
194 |
186 193
|
bitr3d |
|
195 |
|
eleq1 |
|
196 |
195
|
adantr |
|
197 |
194 196
|
imbi12d |
|
198 |
197
|
spc2gv |
|
199 |
184 95 198
|
mp2an |
|
200 |
|
fss |
|
201 |
176 114 200
|
mp2an |
|
202 |
|
fco |
|
203 |
201 202
|
mpan |
|
204 |
|
fssres |
|
205 |
203 122 204
|
syl2an |
|
206 |
205
|
adantlr |
|
207 |
126
|
resabs1d |
|
208 |
|
resco |
|
209 |
207 208
|
eqtrdi |
|
210 |
209
|
adantl |
|
211 |
142
|
simprd |
|
212 |
210 211
|
eqeltrd |
|
213 |
212
|
ralrimiva |
|
214 |
|
reseq2 |
|
215 |
214
|
eleq1d |
|
216 |
215
|
cbvralvw |
|
217 |
213 216
|
sylib |
|
218 |
217
|
adantr |
|
219 |
|
pm2.27 |
|
220 |
206 218 219
|
syl2anc |
|
221 |
199 220
|
mpan9 |
|
222 |
|
resco |
|
223 |
163
|
simplbda |
|
224 |
222 223
|
eqeltrid |
|
225 |
159 224
|
sylan2 |
|
226 |
225
|
ad2antrl |
|
227 |
180 221 226 174
|
mbfres2 |
|
228 |
|
ismbfcn |
|
229 |
228
|
adantr |
|
230 |
229
|
ad2antrl |
|
231 |
175 227 230
|
mpbir2and |
|
232 |
231
|
ex |
|
233 |
232
|
alrimivv |
|
234 |
233
|
a1i |
|
235 |
35 58 65 72 84 234
|
findcard2 |
|
236 |
|
2sp |
|
237 |
2 235 236
|
3syl |
|
238 |
16 25 237
|
vtocl2g |
|
239 |
10 238
|
mpcom |
|
240 |
4 239
|
mpan2d |
|
241 |
1 3 240
|
mp2and |
|