Step |
Hyp |
Ref |
Expression |
1 |
|
addsuniflem.1 |
|
2 |
|
addsuniflem.2 |
|
3 |
|
addsuniflem.3 |
|
4 |
|
addsuniflem.4 |
|
5 |
1
|
scutcld |
|
6 |
3 5
|
eqeltrd |
|
7 |
2
|
scutcld |
|
8 |
4 7
|
eqeltrd |
|
9 |
|
addsval2 |
|
10 |
6 8 9
|
syl2anc |
|
11 |
6 8
|
addscut |
|
12 |
11
|
simp2d |
|
13 |
11
|
simp3d |
|
14 |
|
ovex |
|
15 |
14
|
snnz |
|
16 |
|
sslttr |
|
17 |
15 16
|
mp3an3 |
|
18 |
12 13 17
|
syl2anc |
|
19 |
1 3
|
cofcutr1d |
|
20 |
|
leftssno |
|
21 |
20
|
sseli |
|
22 |
21
|
ad2antlr |
|
23 |
|
ssltss1 |
|
24 |
1 23
|
syl |
|
25 |
24
|
adantr |
|
26 |
25
|
sselda |
|
27 |
8
|
ad2antrr |
|
28 |
22 26 27
|
sleadd1d |
|
29 |
28
|
rexbidva |
|
30 |
29
|
ralbidva |
|
31 |
19 30
|
mpbid |
|
32 |
|
eqeq1 |
|
33 |
32
|
rexbidv |
|
34 |
33
|
rexab |
|
35 |
|
rexcom4 |
|
36 |
|
ovex |
|
37 |
|
breq2 |
|
38 |
36 37
|
ceqsexv |
|
39 |
38
|
rexbii |
|
40 |
|
r19.41v |
|
41 |
40
|
exbii |
|
42 |
35 39 41
|
3bitr3ri |
|
43 |
34 42
|
bitri |
|
44 |
|
ssun1 |
|
45 |
|
ssrexv |
|
46 |
44 45
|
ax-mp |
|
47 |
43 46
|
sylbir |
|
48 |
47
|
ralimi |
|
49 |
31 48
|
syl |
|
50 |
2 4
|
cofcutr1d |
|
51 |
|
leftssno |
|
52 |
51
|
sseli |
|
53 |
52
|
ad2antlr |
|
54 |
|
ssltss1 |
|
55 |
2 54
|
syl |
|
56 |
55
|
adantr |
|
57 |
56
|
sselda |
|
58 |
6
|
ad2antrr |
|
59 |
53 57 58
|
sleadd2d |
|
60 |
59
|
rexbidva |
|
61 |
60
|
ralbidva |
|
62 |
50 61
|
mpbid |
|
63 |
|
eqeq1 |
|
64 |
63
|
rexbidv |
|
65 |
64
|
rexab |
|
66 |
|
rexcom4 |
|
67 |
|
ovex |
|
68 |
|
breq2 |
|
69 |
67 68
|
ceqsexv |
|
70 |
69
|
rexbii |
|
71 |
|
r19.41v |
|
72 |
71
|
exbii |
|
73 |
66 70 72
|
3bitr3ri |
|
74 |
65 73
|
bitri |
|
75 |
|
ssun2 |
|
76 |
|
ssrexv |
|
77 |
75 76
|
ax-mp |
|
78 |
74 77
|
sylbir |
|
79 |
78
|
ralimi |
|
80 |
62 79
|
syl |
|
81 |
|
ralunb |
|
82 |
|
eqeq1 |
|
83 |
82
|
rexbidv |
|
84 |
83
|
ralab |
|
85 |
|
ralcom4 |
|
86 |
|
ovex |
|
87 |
|
breq1 |
|
88 |
87
|
rexbidv |
|
89 |
86 88
|
ceqsalv |
|
90 |
89
|
ralbii |
|
91 |
|
r19.23v |
|
92 |
91
|
albii |
|
93 |
85 90 92
|
3bitr3ri |
|
94 |
84 93
|
bitri |
|
95 |
|
eqeq1 |
|
96 |
95
|
rexbidv |
|
97 |
96
|
ralab |
|
98 |
|
ralcom4 |
|
99 |
|
ovex |
|
100 |
|
breq1 |
|
101 |
100
|
rexbidv |
|
102 |
99 101
|
ceqsalv |
|
103 |
102
|
ralbii |
|
104 |
|
r19.23v |
|
105 |
104
|
albii |
|
106 |
98 103 105
|
3bitr3ri |
|
107 |
97 106
|
bitri |
|
108 |
94 107
|
anbi12i |
|
109 |
81 108
|
bitri |
|
110 |
49 80 109
|
sylanbrc |
|
111 |
1 3
|
cofcutr2d |
|
112 |
|
ssltss2 |
|
113 |
1 112
|
syl |
|
114 |
113
|
adantr |
|
115 |
114
|
sselda |
|
116 |
|
rightssno |
|
117 |
116
|
sseli |
|
118 |
117
|
ad2antlr |
|
119 |
8
|
ad2antrr |
|
120 |
115 118 119
|
sleadd1d |
|
121 |
120
|
rexbidva |
|
122 |
121
|
ralbidva |
|
123 |
111 122
|
mpbid |
|
124 |
|
eqeq1 |
|
125 |
124
|
rexbidv |
|
126 |
125
|
rexab |
|
127 |
|
rexcom4 |
|
128 |
|
ovex |
|
129 |
|
breq1 |
|
130 |
128 129
|
ceqsexv |
|
131 |
130
|
rexbii |
|
132 |
|
r19.41v |
|
133 |
132
|
exbii |
|
134 |
127 131 133
|
3bitr3ri |
|
135 |
126 134
|
bitri |
|
136 |
|
ssun1 |
|
137 |
|
ssrexv |
|
138 |
136 137
|
ax-mp |
|
139 |
135 138
|
sylbir |
|
140 |
139
|
ralimi |
|
141 |
123 140
|
syl |
|
142 |
2 4
|
cofcutr2d |
|
143 |
|
ssltss2 |
|
144 |
2 143
|
syl |
|
145 |
144
|
adantr |
|
146 |
145
|
sselda |
|
147 |
|
rightssno |
|
148 |
147
|
sseli |
|
149 |
148
|
ad2antlr |
|
150 |
6
|
ad2antrr |
|
151 |
146 149 150
|
sleadd2d |
|
152 |
151
|
rexbidva |
|
153 |
152
|
ralbidva |
|
154 |
142 153
|
mpbid |
|
155 |
|
eqeq1 |
|
156 |
155
|
rexbidv |
|
157 |
156
|
rexab |
|
158 |
|
rexcom4 |
|
159 |
|
ovex |
|
160 |
|
breq1 |
|
161 |
159 160
|
ceqsexv |
|
162 |
161
|
rexbii |
|
163 |
|
r19.41v |
|
164 |
163
|
exbii |
|
165 |
158 162 164
|
3bitr3ri |
|
166 |
157 165
|
bitri |
|
167 |
|
ssun2 |
|
168 |
|
ssrexv |
|
169 |
167 168
|
ax-mp |
|
170 |
166 169
|
sylbir |
|
171 |
170
|
ralimi |
|
172 |
154 171
|
syl |
|
173 |
|
ralunb |
|
174 |
|
eqeq1 |
|
175 |
174
|
rexbidv |
|
176 |
175
|
ralab |
|
177 |
|
ralcom4 |
|
178 |
|
ovex |
|
179 |
|
breq2 |
|
180 |
179
|
rexbidv |
|
181 |
178 180
|
ceqsalv |
|
182 |
181
|
ralbii |
|
183 |
|
r19.23v |
|
184 |
183
|
albii |
|
185 |
177 182 184
|
3bitr3ri |
|
186 |
176 185
|
bitri |
|
187 |
|
eqeq1 |
|
188 |
187
|
rexbidv |
|
189 |
188
|
ralab |
|
190 |
|
ralcom4 |
|
191 |
|
ovex |
|
192 |
|
breq2 |
|
193 |
192
|
rexbidv |
|
194 |
191 193
|
ceqsalv |
|
195 |
194
|
ralbii |
|
196 |
|
r19.23v |
|
197 |
196
|
albii |
|
198 |
190 195 197
|
3bitr3ri |
|
199 |
189 198
|
bitri |
|
200 |
186 199
|
anbi12i |
|
201 |
173 200
|
bitri |
|
202 |
141 172 201
|
sylanbrc |
|
203 |
|
eqid |
|
204 |
203
|
rnmpt |
|
205 |
|
ssltex1 |
|
206 |
1 205
|
syl |
|
207 |
206
|
mptexd |
|
208 |
|
rnexg |
|
209 |
207 208
|
syl |
|
210 |
204 209
|
eqeltrrid |
|
211 |
|
eqid |
|
212 |
211
|
rnmpt |
|
213 |
|
ssltex1 |
|
214 |
2 213
|
syl |
|
215 |
214
|
mptexd |
|
216 |
|
rnexg |
|
217 |
215 216
|
syl |
|
218 |
212 217
|
eqeltrrid |
|
219 |
210 218
|
unexd |
|
220 |
|
snex |
|
221 |
220
|
a1i |
|
222 |
24
|
sselda |
|
223 |
8
|
adantr |
|
224 |
222 223
|
addscld |
|
225 |
|
eleq1 |
|
226 |
224 225
|
syl5ibrcom |
|
227 |
226
|
rexlimdva |
|
228 |
227
|
abssdv |
|
229 |
6
|
adantr |
|
230 |
55
|
sselda |
|
231 |
229 230
|
addscld |
|
232 |
|
eleq1 |
|
233 |
231 232
|
syl5ibrcom |
|
234 |
233
|
rexlimdva |
|
235 |
234
|
abssdv |
|
236 |
228 235
|
unssd |
|
237 |
6 8
|
addscld |
|
238 |
237
|
snssd |
|
239 |
|
velsn |
|
240 |
|
elun |
|
241 |
|
vex |
|
242 |
|
eqeq1 |
|
243 |
242
|
rexbidv |
|
244 |
241 243
|
elab |
|
245 |
|
eqeq1 |
|
246 |
245
|
rexbidv |
|
247 |
241 246
|
elab |
|
248 |
244 247
|
orbi12i |
|
249 |
240 248
|
bitri |
|
250 |
|
scutcut |
|
251 |
1 250
|
syl |
|
252 |
251
|
simp2d |
|
253 |
252
|
adantr |
|
254 |
|
simpr |
|
255 |
|
ovex |
|
256 |
255
|
snid |
|
257 |
256
|
a1i |
|
258 |
253 254 257
|
ssltsepcd |
|
259 |
3
|
adantr |
|
260 |
258 259
|
breqtrrd |
|
261 |
6
|
adantr |
|
262 |
222 261 223
|
sltadd1d |
|
263 |
260 262
|
mpbid |
|
264 |
|
breq1 |
|
265 |
263 264
|
syl5ibrcom |
|
266 |
265
|
rexlimdva |
|
267 |
|
scutcut |
|
268 |
2 267
|
syl |
|
269 |
268
|
simp2d |
|
270 |
269
|
adantr |
|
271 |
|
simpr |
|
272 |
|
ovex |
|
273 |
272
|
snid |
|
274 |
273
|
a1i |
|
275 |
270 271 274
|
ssltsepcd |
|
276 |
4
|
adantr |
|
277 |
275 276
|
breqtrrd |
|
278 |
8
|
adantr |
|
279 |
230 278 229
|
sltadd2d |
|
280 |
277 279
|
mpbid |
|
281 |
|
breq1 |
|
282 |
280 281
|
syl5ibrcom |
|
283 |
282
|
rexlimdva |
|
284 |
266 283
|
jaod |
|
285 |
249 284
|
biimtrid |
|
286 |
285
|
imp |
|
287 |
|
breq2 |
|
288 |
286 287
|
syl5ibrcom |
|
289 |
239 288
|
biimtrid |
|
290 |
289
|
3impia |
|
291 |
219 221 236 238 290
|
ssltd |
|
292 |
10
|
sneqd |
|
293 |
291 292
|
breqtrd |
|
294 |
|
eqid |
|
295 |
294
|
rnmpt |
|
296 |
|
ssltex2 |
|
297 |
1 296
|
syl |
|
298 |
297
|
mptexd |
|
299 |
|
rnexg |
|
300 |
298 299
|
syl |
|
301 |
295 300
|
eqeltrrid |
|
302 |
|
eqid |
|
303 |
302
|
rnmpt |
|
304 |
|
ssltex2 |
|
305 |
2 304
|
syl |
|
306 |
305
|
mptexd |
|
307 |
|
rnexg |
|
308 |
306 307
|
syl |
|
309 |
303 308
|
eqeltrrid |
|
310 |
301 309
|
unexd |
|
311 |
113
|
sselda |
|
312 |
8
|
adantr |
|
313 |
311 312
|
addscld |
|
314 |
|
eleq1 |
|
315 |
313 314
|
syl5ibrcom |
|
316 |
315
|
rexlimdva |
|
317 |
316
|
abssdv |
|
318 |
6
|
adantr |
|
319 |
144
|
sselda |
|
320 |
318 319
|
addscld |
|
321 |
|
eleq1 |
|
322 |
320 321
|
syl5ibrcom |
|
323 |
322
|
rexlimdva |
|
324 |
323
|
abssdv |
|
325 |
317 324
|
unssd |
|
326 |
|
velsn |
|
327 |
|
elun |
|
328 |
|
vex |
|
329 |
328 125
|
elab |
|
330 |
328 156
|
elab |
|
331 |
329 330
|
orbi12i |
|
332 |
327 331
|
bitri |
|
333 |
3
|
adantr |
|
334 |
251
|
simp3d |
|
335 |
334
|
adantr |
|
336 |
256
|
a1i |
|
337 |
|
simpr |
|
338 |
335 336 337
|
ssltsepcd |
|
339 |
333 338
|
eqbrtrd |
|
340 |
6
|
adantr |
|
341 |
340 311 312
|
sltadd1d |
|
342 |
339 341
|
mpbid |
|
343 |
|
breq2 |
|
344 |
342 343
|
syl5ibrcom |
|
345 |
344
|
rexlimdva |
|
346 |
4
|
adantr |
|
347 |
268
|
simp3d |
|
348 |
347
|
adantr |
|
349 |
273
|
a1i |
|
350 |
|
simpr |
|
351 |
348 349 350
|
ssltsepcd |
|
352 |
346 351
|
eqbrtrd |
|
353 |
8
|
adantr |
|
354 |
353 319 318
|
sltadd2d |
|
355 |
352 354
|
mpbid |
|
356 |
|
breq2 |
|
357 |
355 356
|
syl5ibrcom |
|
358 |
357
|
rexlimdva |
|
359 |
345 358
|
jaod |
|
360 |
332 359
|
biimtrid |
|
361 |
360
|
imp |
|
362 |
|
breq1 |
|
363 |
361 362
|
syl5ibrcom |
|
364 |
363
|
ex |
|
365 |
364
|
com23 |
|
366 |
326 365
|
biimtrid |
|
367 |
366
|
3imp |
|
368 |
221 310 238 325 367
|
ssltd |
|
369 |
292 368
|
eqbrtrrd |
|
370 |
18 110 202 293 369
|
cofcut1d |
|
371 |
10 370
|
eqtrd |
|