Step |
Hyp |
Ref |
Expression |
1 |
|
mzpcompact2lem.i |
|
2 |
|
tru |
|
3 |
|
0fin |
|
4 |
|
0ex |
|
5 |
|
mzpconst |
|
6 |
4 5
|
mpan |
|
7 |
|
0ss |
|
8 |
7
|
a1i |
|
9 |
|
fconstmpt |
|
10 |
|
simpr |
|
11 |
|
elmapssres |
|
12 |
10 7 11
|
sylancl |
|
13 |
|
vex |
|
14 |
13
|
fvconst2 |
|
15 |
12 14
|
syl |
|
16 |
15
|
mpteq2dva |
|
17 |
9 16
|
eqtr4id |
|
18 |
|
fveq1 |
|
19 |
18
|
mpteq2dv |
|
20 |
19
|
eqeq2d |
|
21 |
20
|
anbi2d |
|
22 |
21
|
rspcev |
|
23 |
6 8 17 22
|
syl12anc |
|
24 |
|
fveq2 |
|
25 |
|
sseq1 |
|
26 |
|
reseq2 |
|
27 |
26
|
fveq2d |
|
28 |
27
|
mpteq2dv |
|
29 |
28
|
eqeq2d |
|
30 |
25 29
|
anbi12d |
|
31 |
24 30
|
rexeqbidv |
|
32 |
31
|
rspcev |
|
33 |
3 23 32
|
sylancr |
|
34 |
33
|
adantl |
|
35 |
|
snfi |
|
36 |
|
snex |
|
37 |
|
vsnid |
|
38 |
|
mzpproj |
|
39 |
36 37 38
|
mp2an |
|
40 |
39
|
a1i |
|
41 |
|
snssi |
|
42 |
|
fveq1 |
|
43 |
42
|
cbvmptv |
|
44 |
|
simpr |
|
45 |
|
simpl |
|
46 |
45
|
snssd |
|
47 |
|
elmapssres |
|
48 |
44 46 47
|
syl2anc |
|
49 |
|
fveq1 |
|
50 |
|
eqid |
|
51 |
|
fvex |
|
52 |
49 50 51
|
fvmpt |
|
53 |
48 52
|
syl |
|
54 |
|
fvres |
|
55 |
37 54
|
ax-mp |
|
56 |
53 55
|
eqtr2di |
|
57 |
56
|
mpteq2dva |
|
58 |
43 57
|
syl5eq |
|
59 |
|
fveq1 |
|
60 |
59
|
mpteq2dv |
|
61 |
60
|
eqeq2d |
|
62 |
61
|
anbi2d |
|
63 |
62
|
rspcev |
|
64 |
40 41 58 63
|
syl12anc |
|
65 |
|
fveq2 |
|
66 |
|
sseq1 |
|
67 |
|
reseq2 |
|
68 |
67
|
fveq2d |
|
69 |
68
|
mpteq2dv |
|
70 |
69
|
eqeq2d |
|
71 |
66 70
|
anbi12d |
|
72 |
65 71
|
rexeqbidv |
|
73 |
72
|
rspcev |
|
74 |
35 64 73
|
sylancr |
|
75 |
74
|
adantl |
|
76 |
|
simplll |
|
77 |
|
simprll |
|
78 |
|
unfi |
|
79 |
76 77 78
|
syl2anc |
|
80 |
|
vex |
|
81 |
|
vex |
|
82 |
80 81
|
unex |
|
83 |
82
|
a1i |
|
84 |
|
ssun1 |
|
85 |
84
|
a1i |
|
86 |
|
simpllr |
|
87 |
|
mzpresrename |
|
88 |
83 85 86 87
|
syl3anc |
|
89 |
|
ssun2 |
|
90 |
89
|
a1i |
|
91 |
|
simprlr |
|
92 |
|
mzpresrename |
|
93 |
83 90 91 92
|
syl3anc |
|
94 |
|
mzpaddmpt |
|
95 |
88 93 94
|
syl2anc |
|
96 |
|
simplr |
|
97 |
|
simprr |
|
98 |
96 97
|
unssd |
|
99 |
|
ovex |
|
100 |
99
|
a1i |
|
101 |
1
|
a1i |
|
102 |
|
mzpresrename |
|
103 |
101 96 86 102
|
syl3anc |
|
104 |
|
mzpf |
|
105 |
|
ffn |
|
106 |
103 104 105
|
3syl |
|
107 |
|
mzpresrename |
|
108 |
101 97 91 107
|
syl3anc |
|
109 |
|
mzpf |
|
110 |
|
ffn |
|
111 |
108 109 110
|
3syl |
|
112 |
|
ofmpteq |
|
113 |
100 106 111 112
|
syl3anc |
|
114 |
|
elmapi |
|
115 |
|
fssres |
|
116 |
114 98 115
|
syl2anr |
|
117 |
|
zex |
|
118 |
117 82
|
elmap |
|
119 |
116 118
|
sylibr |
|
120 |
|
reseq1 |
|
121 |
120
|
fveq2d |
|
122 |
|
reseq1 |
|
123 |
122
|
fveq2d |
|
124 |
121 123
|
oveq12d |
|
125 |
|
eqid |
|
126 |
|
ovex |
|
127 |
124 125 126
|
fvmpt |
|
128 |
119 127
|
syl |
|
129 |
|
resabs1 |
|
130 |
84 129
|
ax-mp |
|
131 |
130
|
fveq2i |
|
132 |
|
resabs1 |
|
133 |
89 132
|
ax-mp |
|
134 |
133
|
fveq2i |
|
135 |
131 134
|
oveq12i |
|
136 |
128 135
|
eqtr2di |
|
137 |
136
|
mpteq2dva |
|
138 |
113 137
|
eqtrd |
|
139 |
|
fveq1 |
|
140 |
139
|
mpteq2dv |
|
141 |
140
|
eqeq2d |
|
142 |
141
|
anbi2d |
|
143 |
142
|
rspcev |
|
144 |
95 98 138 143
|
syl12anc |
|
145 |
|
mzpmulmpt |
|
146 |
88 93 145
|
syl2anc |
|
147 |
|
ofmpteq |
|
148 |
100 106 111 147
|
syl3anc |
|
149 |
121 123
|
oveq12d |
|
150 |
|
eqid |
|
151 |
|
ovex |
|
152 |
149 150 151
|
fvmpt |
|
153 |
119 152
|
syl |
|
154 |
131 134
|
oveq12i |
|
155 |
153 154
|
eqtr2di |
|
156 |
155
|
mpteq2dva |
|
157 |
148 156
|
eqtrd |
|
158 |
|
fveq1 |
|
159 |
158
|
mpteq2dv |
|
160 |
159
|
eqeq2d |
|
161 |
160
|
anbi2d |
|
162 |
161
|
rspcev |
|
163 |
146 98 157 162
|
syl12anc |
|
164 |
|
fveq2 |
|
165 |
|
sseq1 |
|
166 |
|
reseq2 |
|
167 |
166
|
fveq2d |
|
168 |
167
|
mpteq2dv |
|
169 |
168
|
eqeq2d |
|
170 |
165 169
|
anbi12d |
|
171 |
164 170
|
rexeqbidv |
|
172 |
168
|
eqeq2d |
|
173 |
165 172
|
anbi12d |
|
174 |
164 173
|
rexeqbidv |
|
175 |
171 174
|
anbi12d |
|
176 |
175
|
rspcev |
|
177 |
79 144 163 176
|
syl12anc |
|
178 |
177
|
adantlrr |
|
179 |
178
|
adantrrr |
|
180 |
|
simplrr |
|
181 |
|
simprrr |
|
182 |
180 181
|
oveq12d |
|
183 |
182
|
eqeq1d |
|
184 |
183
|
anbi2d |
|
185 |
184
|
rexbidv |
|
186 |
180 181
|
oveq12d |
|
187 |
186
|
eqeq1d |
|
188 |
187
|
anbi2d |
|
189 |
188
|
rexbidv |
|
190 |
185 189
|
anbi12d |
|
191 |
190
|
rexbidv |
|
192 |
179 191
|
mpbird |
|
193 |
|
r19.40 |
|
194 |
192 193
|
syl |
|
195 |
194
|
exp32 |
|
196 |
195
|
rexlimdvv |
|
197 |
196
|
ex |
|
198 |
197
|
rexlimivv |
|
199 |
198
|
imp |
|
200 |
199
|
ad2ant2l |
|
201 |
200
|
3adant1 |
|
202 |
201
|
simpld |
|
203 |
201
|
simprd |
|
204 |
|
eqeq1 |
|
205 |
204
|
anbi2d |
|
206 |
205
|
2rexbidv |
|
207 |
|
eqeq1 |
|
208 |
207
|
anbi2d |
|
209 |
208
|
2rexbidv |
|
210 |
|
eqeq1 |
|
211 |
210
|
anbi2d |
|
212 |
211
|
2rexbidv |
|
213 |
|
fveq2 |
|
214 |
|
sseq1 |
|
215 |
|
reseq2 |
|
216 |
215
|
fveq2d |
|
217 |
216
|
mpteq2dv |
|
218 |
217
|
eqeq2d |
|
219 |
214 218
|
anbi12d |
|
220 |
213 219
|
rexeqbidv |
|
221 |
|
fveq1 |
|
222 |
221
|
mpteq2dv |
|
223 |
222
|
eqeq2d |
|
224 |
223
|
anbi2d |
|
225 |
224
|
cbvrexvw |
|
226 |
220 225
|
bitrdi |
|
227 |
226
|
cbvrexvw |
|
228 |
212 227
|
bitrdi |
|
229 |
|
eqeq1 |
|
230 |
229
|
anbi2d |
|
231 |
230
|
2rexbidv |
|
232 |
|
fveq2 |
|
233 |
|
sseq1 |
|
234 |
|
reseq2 |
|
235 |
234
|
fveq2d |
|
236 |
235
|
mpteq2dv |
|
237 |
236
|
eqeq2d |
|
238 |
233 237
|
anbi12d |
|
239 |
232 238
|
rexeqbidv |
|
240 |
|
fveq1 |
|
241 |
240
|
mpteq2dv |
|
242 |
241
|
eqeq2d |
|
243 |
242
|
anbi2d |
|
244 |
243
|
cbvrexvw |
|
245 |
239 244
|
bitrdi |
|
246 |
245
|
cbvrexvw |
|
247 |
231 246
|
bitrdi |
|
248 |
|
eqeq1 |
|
249 |
248
|
anbi2d |
|
250 |
249
|
2rexbidv |
|
251 |
|
eqeq1 |
|
252 |
251
|
anbi2d |
|
253 |
252
|
2rexbidv |
|
254 |
|
eqeq1 |
|
255 |
254
|
anbi2d |
|
256 |
255
|
2rexbidv |
|
257 |
34 75 202 203 206 209 228 247 250 253 256
|
mzpindd |
|
258 |
2 257
|
mpan |
|
259 |
|
reseq1 |
|
260 |
259
|
fveq2d |
|
261 |
260
|
cbvmptv |
|
262 |
261
|
eqeq2i |
|
263 |
262
|
anbi2i |
|
264 |
263
|
2rexbii |
|
265 |
258 264
|
sylib |
|