Step |
Hyp |
Ref |
Expression |
1 |
|
elpwi |
|
2 |
|
0ss |
|
3 |
|
0fin |
|
4 |
|
elfpw |
|
5 |
2 3 4
|
mpbir2an |
|
6 |
|
simprr |
|
7 |
|
simprl |
|
8 |
7
|
unieqd |
|
9 |
6 8
|
eqtrd |
|
10 |
|
unieq |
|
11 |
10
|
rspceeqv |
|
12 |
5 9 11
|
sylancr |
|
13 |
12
|
expr |
|
14 |
|
vn0 |
|
15 |
|
iineq1 |
|
16 |
15
|
adantl |
|
17 |
|
0iin |
|
18 |
16 17
|
eqtrdi |
|
19 |
18
|
eqeq1d |
|
20 |
19
|
necon3bbid |
|
21 |
14 20
|
mpbiri |
|
22 |
21
|
pm2.21d |
|
23 |
13 22
|
2thd |
|
24 |
|
uniss |
|
25 |
24
|
ad2antlr |
|
26 |
|
eqss |
|
27 |
26
|
baib |
|
28 |
25 27
|
syl |
|
29 |
|
eqcom |
|
30 |
|
ssdif0 |
|
31 |
28 29 30
|
3bitr3g |
|
32 |
|
iindif2 |
|
33 |
32
|
adantl |
|
34 |
|
uniiun |
|
35 |
34
|
difeq2i |
|
36 |
33 35
|
eqtr4di |
|
37 |
36
|
eqeq1d |
|
38 |
31 37
|
bitr4d |
|
39 |
|
imassrn |
|
40 |
|
df-ima |
|
41 |
|
resmpt |
|
42 |
41
|
adantl |
|
43 |
42
|
rneqd |
|
44 |
40 43
|
syl5eq |
|
45 |
44
|
ad2antrr |
|
46 |
39 45
|
sseqtrrid |
|
47 |
|
funmpt |
|
48 |
|
elinel2 |
|
49 |
48
|
adantl |
|
50 |
|
imafi |
|
51 |
47 49 50
|
sylancr |
|
52 |
|
elfpw |
|
53 |
46 51 52
|
sylanbrc |
|
54 |
|
eqid |
|
55 |
54
|
topopn |
|
56 |
|
difexg |
|
57 |
55 56
|
syl |
|
58 |
57
|
ralrimivw |
|
59 |
|
eqid |
|
60 |
59
|
fnmpt |
|
61 |
58 60
|
syl |
|
62 |
61
|
ad3antrrr |
|
63 |
|
simpr |
|
64 |
|
elfpw |
|
65 |
63 64
|
sylib |
|
66 |
65
|
simpld |
|
67 |
44
|
ad2antrr |
|
68 |
66 67
|
sseqtrd |
|
69 |
65
|
simprd |
|
70 |
|
fipreima |
|
71 |
62 68 69 70
|
syl3anc |
|
72 |
|
eqcom |
|
73 |
72
|
rexbii |
|
74 |
71 73
|
sylib |
|
75 |
|
simpr |
|
76 |
75
|
inteqd |
|
77 |
76
|
eqeq2d |
|
78 |
53 74 77
|
rexxfrd |
|
79 |
|
0ex |
|
80 |
|
imassrn |
|
81 |
|
eqid |
|
82 |
54 81
|
opncldf1 |
|
83 |
82
|
simpld |
|
84 |
|
f1ofo |
|
85 |
83 84
|
syl |
|
86 |
|
forn |
|
87 |
85 86
|
syl |
|
88 |
80 87
|
sseqtrid |
|
89 |
|
fvex |
|
90 |
89
|
elpw2 |
|
91 |
88 90
|
sylibr |
|
92 |
91
|
ad2antrr |
|
93 |
|
elfi |
|
94 |
79 92 93
|
sylancr |
|
95 |
|
inundif |
|
96 |
95
|
rexeqi |
|
97 |
|
rexun |
|
98 |
96 97
|
bitr3i |
|
99 |
|
elinel2 |
|
100 |
|
elsni |
|
101 |
99 100
|
syl |
|
102 |
101
|
unieqd |
|
103 |
|
uni0 |
|
104 |
102 103
|
eqtrdi |
|
105 |
104
|
eqeq2d |
|
106 |
105
|
biimpd |
|
107 |
106
|
rexlimiv |
|
108 |
|
ssidd |
|
109 |
|
simprr |
|
110 |
|
0ss |
|
111 |
109 110
|
eqsstrdi |
|
112 |
24
|
ad2antlr |
|
113 |
111 112
|
eqssd |
|
114 |
113 109
|
eqtr3d |
|
115 |
114 3
|
eqeltrdi |
|
116 |
|
pwfi |
|
117 |
115 116
|
sylib |
|
118 |
|
pwuni |
|
119 |
|
ssfi |
|
120 |
117 118 119
|
sylancl |
|
121 |
|
elfpw |
|
122 |
108 120 121
|
sylanbrc |
|
123 |
|
simprl |
|
124 |
|
eldifsn |
|
125 |
122 123 124
|
sylanbrc |
|
126 |
|
unieq |
|
127 |
126
|
rspceeqv |
|
128 |
125 113 127
|
syl2anc |
|
129 |
128
|
expr |
|
130 |
107 129
|
syl5 |
|
131 |
|
idd |
|
132 |
130 131
|
jaod |
|
133 |
|
olc |
|
134 |
132 133
|
impbid1 |
|
135 |
98 134
|
syl5bb |
|
136 |
|
eldifi |
|
137 |
136
|
adantl |
|
138 |
|
elfpw |
|
139 |
137 138
|
sylib |
|
140 |
139
|
simpld |
|
141 |
|
simpllr |
|
142 |
140 141
|
sstrd |
|
143 |
142
|
unissd |
|
144 |
|
eqss |
|
145 |
144
|
baib |
|
146 |
143 145
|
syl |
|
147 |
|
eqcom |
|
148 |
|
ssdif0 |
|
149 |
|
eqcom |
|
150 |
148 149
|
bitri |
|
151 |
146 147 150
|
3bitr3g |
|
152 |
|
df-ima |
|
153 |
140
|
resmptd |
|
154 |
153
|
rneqd |
|
155 |
152 154
|
syl5eq |
|
156 |
155
|
inteqd |
|
157 |
57
|
ralrimivw |
|
158 |
157
|
ad3antrrr |
|
159 |
|
dfiin3g |
|
160 |
158 159
|
syl |
|
161 |
|
eldifsni |
|
162 |
161
|
adantl |
|
163 |
|
iindif2 |
|
164 |
162 163
|
syl |
|
165 |
156 160 164
|
3eqtr2d |
|
166 |
|
uniiun |
|
167 |
166
|
difeq2i |
|
168 |
165 167
|
eqtr4di |
|
169 |
168
|
eqeq2d |
|
170 |
151 169
|
bitr4d |
|
171 |
170
|
rexbidva |
|
172 |
135 171
|
bitrd |
|
173 |
|
imaeq2 |
|
174 |
|
ima0 |
|
175 |
173 174
|
eqtrdi |
|
176 |
175
|
inteqd |
|
177 |
|
int0 |
|
178 |
176 177
|
eqtrdi |
|
179 |
178
|
neeq1d |
|
180 |
14 179
|
mpbiri |
|
181 |
180
|
necomd |
|
182 |
181
|
necon2i |
|
183 |
|
eldifsn |
|
184 |
183
|
rbaibr |
|
185 |
182 184
|
syl |
|
186 |
185
|
pm5.32ri |
|
187 |
186
|
rexbii2 |
|
188 |
172 187
|
bitr4di |
|
189 |
78 94 188
|
3bitr4rd |
|
190 |
38 189
|
imbi12d |
|
191 |
23 190
|
pm2.61dane |
|
192 |
58
|
adantr |
|
193 |
|
dfiin3g |
|
194 |
192 193
|
syl |
|
195 |
44
|
inteqd |
|
196 |
194 195
|
eqtr4d |
|
197 |
196
|
eqeq1d |
|
198 |
|
nne |
|
199 |
197 198
|
bitr4di |
|
200 |
199
|
imbi1d |
|
201 |
191 200
|
bitrd |
|
202 |
|
con1b |
|
203 |
201 202
|
bitrdi |
|
204 |
1 203
|
sylan2 |
|
205 |
204
|
ralbidva |
|
206 |
54
|
iscmp |
|
207 |
206
|
baib |
|
208 |
91
|
adantr |
|
209 |
|
simpl |
|
210 |
|
funmpt |
|
211 |
210
|
a1i |
|
212 |
|
elpwi |
|
213 |
|
foima |
|
214 |
85 213
|
syl |
|
215 |
214
|
sseq2d |
|
216 |
212 215
|
syl5ibr |
|
217 |
216
|
imp |
|
218 |
|
ssimaexg |
|
219 |
209 211 217 218
|
syl3anc |
|
220 |
|
df-rex |
|
221 |
|
velpw |
|
222 |
221
|
anbi1i |
|
223 |
222
|
exbii |
|
224 |
220 223
|
bitri |
|
225 |
219 224
|
sylibr |
|
226 |
|
simpr |
|
227 |
226
|
fveq2d |
|
228 |
227
|
eleq2d |
|
229 |
228
|
notbid |
|
230 |
226
|
inteqd |
|
231 |
230
|
neeq1d |
|
232 |
229 231
|
imbi12d |
|
233 |
208 225 232
|
ralxfrd |
|
234 |
205 207 233
|
3bitr4d |
|