Step |
Hyp |
Ref |
Expression |
1 |
|
poimir.0 |
|
2 |
|
poimirlem22.s |
|
3 |
|
poimirlem22.1 |
|
4 |
|
poimirlem12.2 |
|
5 |
|
poimirlem11.3 |
|
6 |
|
poimirlem11.4 |
|
7 |
|
poimirlem11.5 |
|
8 |
|
poimirlem11.6 |
|
9 |
|
eldif |
|
10 |
|
imassrn |
|
11 |
|
elrabi |
|
12 |
11 2
|
eleq2s |
|
13 |
4 12
|
syl |
|
14 |
|
xp1st |
|
15 |
13 14
|
syl |
|
16 |
|
xp2nd |
|
17 |
15 16
|
syl |
|
18 |
|
fvex |
|
19 |
|
f1oeq1 |
|
20 |
18 19
|
elab |
|
21 |
17 20
|
sylib |
|
22 |
|
f1of |
|
23 |
21 22
|
syl |
|
24 |
23
|
frnd |
|
25 |
10 24
|
sstrid |
|
26 |
|
elrabi |
|
27 |
26 2
|
eleq2s |
|
28 |
6 27
|
syl |
|
29 |
|
xp1st |
|
30 |
28 29
|
syl |
|
31 |
|
xp2nd |
|
32 |
30 31
|
syl |
|
33 |
|
fvex |
|
34 |
|
f1oeq1 |
|
35 |
33 34
|
elab |
|
36 |
32 35
|
sylib |
|
37 |
|
f1ofo |
|
38 |
36 37
|
syl |
|
39 |
|
foima |
|
40 |
38 39
|
syl |
|
41 |
25 40
|
sseqtrrd |
|
42 |
41
|
ssdifd |
|
43 |
|
dff1o3 |
|
44 |
43
|
simprbi |
|
45 |
36 44
|
syl |
|
46 |
|
imadif |
|
47 |
45 46
|
syl |
|
48 |
|
difun2 |
|
49 |
|
fzsplit |
|
50 |
8 49
|
syl |
|
51 |
|
uncom |
|
52 |
50 51
|
eqtrdi |
|
53 |
52
|
difeq1d |
|
54 |
|
incom |
|
55 |
|
elfznn |
|
56 |
8 55
|
syl |
|
57 |
56
|
nnred |
|
58 |
57
|
ltp1d |
|
59 |
|
fzdisj |
|
60 |
58 59
|
syl |
|
61 |
54 60
|
syl5eq |
|
62 |
|
disj3 |
|
63 |
61 62
|
sylib |
|
64 |
48 53 63
|
3eqtr4a |
|
65 |
64
|
imaeq2d |
|
66 |
47 65
|
eqtr3d |
|
67 |
42 66
|
sseqtrd |
|
68 |
67
|
sselda |
|
69 |
9 68
|
sylan2br |
|
70 |
|
fveq2 |
|
71 |
70
|
breq2d |
|
72 |
71
|
ifbid |
|
73 |
72
|
csbeq1d |
|
74 |
|
2fveq3 |
|
75 |
|
2fveq3 |
|
76 |
75
|
imaeq1d |
|
77 |
76
|
xpeq1d |
|
78 |
75
|
imaeq1d |
|
79 |
78
|
xpeq1d |
|
80 |
77 79
|
uneq12d |
|
81 |
74 80
|
oveq12d |
|
82 |
81
|
csbeq2dv |
|
83 |
73 82
|
eqtrd |
|
84 |
83
|
mpteq2dv |
|
85 |
84
|
eqeq2d |
|
86 |
85 2
|
elrab2 |
|
87 |
86
|
simprbi |
|
88 |
6 87
|
syl |
|
89 |
|
breq12 |
|
90 |
7 89
|
sylan2 |
|
91 |
90
|
ancoms |
|
92 |
|
oveq1 |
|
93 |
56
|
nncnd |
|
94 |
|
npcan1 |
|
95 |
93 94
|
syl |
|
96 |
92 95
|
sylan9eqr |
|
97 |
91 96
|
ifbieq2d |
|
98 |
56
|
nnzd |
|
99 |
1
|
nnzd |
|
100 |
|
elfzm1b |
|
101 |
98 99 100
|
syl2anc |
|
102 |
8 101
|
mpbid |
|
103 |
|
elfzle1 |
|
104 |
102 103
|
syl |
|
105 |
|
0red |
|
106 |
|
nnm1nn0 |
|
107 |
56 106
|
syl |
|
108 |
107
|
nn0red |
|
109 |
105 108
|
lenltd |
|
110 |
104 109
|
mpbid |
|
111 |
110
|
iffalsed |
|
112 |
111
|
adantr |
|
113 |
97 112
|
eqtrd |
|
114 |
113
|
csbeq1d |
|
115 |
|
oveq2 |
|
116 |
115
|
imaeq2d |
|
117 |
116
|
xpeq1d |
|
118 |
|
oveq1 |
|
119 |
118
|
oveq1d |
|
120 |
119
|
imaeq2d |
|
121 |
120
|
xpeq1d |
|
122 |
117 121
|
uneq12d |
|
123 |
122
|
oveq2d |
|
124 |
123
|
adantl |
|
125 |
8 124
|
csbied |
|
126 |
125
|
adantr |
|
127 |
114 126
|
eqtrd |
|
128 |
|
ovexd |
|
129 |
88 127 102 128
|
fvmptd |
|
130 |
129
|
fveq1d |
|
131 |
130
|
adantr |
|
132 |
|
imassrn |
|
133 |
|
f1of |
|
134 |
36 133
|
syl |
|
135 |
134
|
frnd |
|
136 |
132 135
|
sstrid |
|
137 |
136
|
sselda |
|
138 |
|
xp1st |
|
139 |
30 138
|
syl |
|
140 |
|
elmapfn |
|
141 |
139 140
|
syl |
|
142 |
141
|
adantr |
|
143 |
|
1ex |
|
144 |
|
fnconstg |
|
145 |
143 144
|
ax-mp |
|
146 |
|
c0ex |
|
147 |
|
fnconstg |
|
148 |
146 147
|
ax-mp |
|
149 |
145 148
|
pm3.2i |
|
150 |
|
imain |
|
151 |
45 150
|
syl |
|
152 |
60
|
imaeq2d |
|
153 |
|
ima0 |
|
154 |
152 153
|
eqtrdi |
|
155 |
151 154
|
eqtr3d |
|
156 |
|
fnun |
|
157 |
149 155 156
|
sylancr |
|
158 |
|
imaundi |
|
159 |
50
|
imaeq2d |
|
160 |
159 40
|
eqtr3d |
|
161 |
158 160
|
syl5eqr |
|
162 |
161
|
fneq2d |
|
163 |
157 162
|
mpbid |
|
164 |
163
|
adantr |
|
165 |
|
ovexd |
|
166 |
|
inidm |
|
167 |
|
eqidd |
|
168 |
|
fvun2 |
|
169 |
145 148 168
|
mp3an12 |
|
170 |
155 169
|
sylan |
|
171 |
146
|
fvconst2 |
|
172 |
171
|
adantl |
|
173 |
170 172
|
eqtrd |
|
174 |
173
|
adantr |
|
175 |
142 164 165 165 166 167 174
|
ofval |
|
176 |
137 175
|
mpdan |
|
177 |
|
elmapi |
|
178 |
139 177
|
syl |
|
179 |
178
|
ffvelrnda |
|
180 |
|
elfzonn0 |
|
181 |
179 180
|
syl |
|
182 |
181
|
nn0cnd |
|
183 |
137 182
|
syldan |
|
184 |
183
|
addid1d |
|
185 |
131 176 184
|
3eqtrd |
|
186 |
69 185
|
syldan |
|
187 |
|
fveq2 |
|
188 |
187
|
breq2d |
|
189 |
188
|
ifbid |
|
190 |
189
|
csbeq1d |
|
191 |
|
2fveq3 |
|
192 |
|
2fveq3 |
|
193 |
192
|
imaeq1d |
|
194 |
193
|
xpeq1d |
|
195 |
192
|
imaeq1d |
|
196 |
195
|
xpeq1d |
|
197 |
194 196
|
uneq12d |
|
198 |
191 197
|
oveq12d |
|
199 |
198
|
csbeq2dv |
|
200 |
190 199
|
eqtrd |
|
201 |
200
|
mpteq2dv |
|
202 |
201
|
eqeq2d |
|
203 |
202 2
|
elrab2 |
|
204 |
203
|
simprbi |
|
205 |
4 204
|
syl |
|
206 |
|
breq12 |
|
207 |
5 206
|
sylan2 |
|
208 |
207
|
ancoms |
|
209 |
208 96
|
ifbieq2d |
|
210 |
209 112
|
eqtrd |
|
211 |
210
|
csbeq1d |
|
212 |
115
|
imaeq2d |
|
213 |
212
|
xpeq1d |
|
214 |
119
|
imaeq2d |
|
215 |
214
|
xpeq1d |
|
216 |
213 215
|
uneq12d |
|
217 |
216
|
oveq2d |
|
218 |
217
|
adantl |
|
219 |
8 218
|
csbied |
|
220 |
219
|
adantr |
|
221 |
211 220
|
eqtrd |
|
222 |
|
ovexd |
|
223 |
205 221 102 222
|
fvmptd |
|
224 |
223
|
fveq1d |
|
225 |
224
|
adantr |
|
226 |
25
|
sselda |
|
227 |
|
xp1st |
|
228 |
15 227
|
syl |
|
229 |
|
elmapfn |
|
230 |
228 229
|
syl |
|
231 |
230
|
adantr |
|
232 |
|
fnconstg |
|
233 |
143 232
|
ax-mp |
|
234 |
|
fnconstg |
|
235 |
146 234
|
ax-mp |
|
236 |
233 235
|
pm3.2i |
|
237 |
|
dff1o3 |
|
238 |
237
|
simprbi |
|
239 |
21 238
|
syl |
|
240 |
|
imain |
|
241 |
239 240
|
syl |
|
242 |
60
|
imaeq2d |
|
243 |
|
ima0 |
|
244 |
242 243
|
eqtrdi |
|
245 |
241 244
|
eqtr3d |
|
246 |
|
fnun |
|
247 |
236 245 246
|
sylancr |
|
248 |
|
imaundi |
|
249 |
50
|
imaeq2d |
|
250 |
|
f1ofo |
|
251 |
21 250
|
syl |
|
252 |
|
foima |
|
253 |
251 252
|
syl |
|
254 |
249 253
|
eqtr3d |
|
255 |
248 254
|
syl5eqr |
|
256 |
255
|
fneq2d |
|
257 |
247 256
|
mpbid |
|
258 |
257
|
adantr |
|
259 |
|
ovexd |
|
260 |
|
eqidd |
|
261 |
|
fvun1 |
|
262 |
233 235 261
|
mp3an12 |
|
263 |
245 262
|
sylan |
|
264 |
143
|
fvconst2 |
|
265 |
264
|
adantl |
|
266 |
263 265
|
eqtrd |
|
267 |
266
|
adantr |
|
268 |
231 258 259 259 166 260 267
|
ofval |
|
269 |
226 268
|
mpdan |
|
270 |
225 269
|
eqtrd |
|
271 |
270
|
adantrr |
|
272 |
1 2 3 6 7
|
poimirlem10 |
|
273 |
1 2 3 4 5
|
poimirlem10 |
|
274 |
272 273
|
eqtr3d |
|
275 |
274
|
fveq1d |
|
276 |
275
|
adantr |
|
277 |
186 271 276
|
3eqtr3d |
|
278 |
|
elmapi |
|
279 |
228 278
|
syl |
|
280 |
279
|
ffvelrnda |
|
281 |
|
elfzonn0 |
|
282 |
280 281
|
syl |
|
283 |
282
|
nn0red |
|
284 |
283
|
ltp1d |
|
285 |
283 284
|
gtned |
|
286 |
226 285
|
syldan |
|
287 |
286
|
neneqd |
|
288 |
287
|
adantrr |
|
289 |
277 288
|
pm2.65da |
|
290 |
|
iman |
|
291 |
289 290
|
sylibr |
|
292 |
291
|
ssrdv |
|