Step |
Hyp |
Ref |
Expression |
1 |
|
mulsproplem.1 |
|
2 |
|
mulsproplem.2 |
|
3 |
|
mulsproplem.3 |
|
4 |
|
mulsproplem.4 |
|
5 |
|
mulsproplem.5 |
|
6 |
|
mulsproplem.6 |
|
7 |
|
mulsproplem.7 |
|
8 |
|
mulsproplem12.1 |
|
9 |
|
mulsproplem12.2 |
|
10 |
|
unidm |
|
11 |
|
unidm |
|
12 |
|
bday0s |
|
13 |
12 12
|
oveq12i |
|
14 |
|
0elon |
|
15 |
|
naddrid |
|
16 |
14 15
|
ax-mp |
|
17 |
13 16
|
eqtri |
|
18 |
11 17
|
eqtri |
|
19 |
10 18
|
eqtri |
|
20 |
19
|
uneq2i |
|
21 |
|
un0 |
|
22 |
20 21
|
eqtri |
|
23 |
|
ssun2 |
|
24 |
|
ssun1 |
|
25 |
23 24
|
sstri |
|
26 |
|
ssun2 |
|
27 |
25 26
|
sstri |
|
28 |
22 27
|
eqsstri |
|
29 |
28
|
sseli |
|
30 |
29
|
imim1i |
|
31 |
30
|
6ralimi |
|
32 |
1 31
|
syl |
|
33 |
32 3 5
|
mulsproplem10 |
|
34 |
33
|
simp2d |
|
35 |
34
|
adantr |
|
36 |
|
simprl |
|
37 |
|
bdayelon |
|
38 |
2
|
adantr |
|
39 |
|
oldbday |
|
40 |
37 38 39
|
sylancr |
|
41 |
36 40
|
mpbird |
|
42 |
6
|
adantr |
|
43 |
|
breq1 |
|
44 |
|
leftval |
|
45 |
43 44
|
elrab2 |
|
46 |
41 42 45
|
sylanbrc |
|
47 |
|
simprr |
|
48 |
|
bdayelon |
|
49 |
4
|
adantr |
|
50 |
|
oldbday |
|
51 |
48 49 50
|
sylancr |
|
52 |
47 51
|
mpbird |
|
53 |
7
|
adantr |
|
54 |
|
breq1 |
|
55 |
|
leftval |
|
56 |
54 55
|
elrab2 |
|
57 |
52 53 56
|
sylanbrc |
|
58 |
|
eqid |
|
59 |
|
oveq1 |
|
60 |
59
|
oveq1d |
|
61 |
|
oveq1 |
|
62 |
60 61
|
oveq12d |
|
63 |
62
|
eqeq2d |
|
64 |
|
oveq2 |
|
65 |
64
|
oveq2d |
|
66 |
|
oveq2 |
|
67 |
65 66
|
oveq12d |
|
68 |
67
|
eqeq2d |
|
69 |
63 68
|
rspc2ev |
|
70 |
58 69
|
mp3an3 |
|
71 |
46 57 70
|
syl2anc |
|
72 |
|
ovex |
|
73 |
|
eqeq1 |
|
74 |
73
|
2rexbidv |
|
75 |
72 74
|
elab |
|
76 |
71 75
|
sylibr |
|
77 |
|
elun1 |
|
78 |
76 77
|
syl |
|
79 |
|
ovex |
|
80 |
79
|
snid |
|
81 |
80
|
a1i |
|
82 |
35 78 81
|
ssltsepcd |
|
83 |
19
|
uneq2i |
|
84 |
|
un0 |
|
85 |
83 84
|
eqtri |
|
86 |
|
ssun1 |
|
87 |
|
ssun2 |
|
88 |
86 87
|
sstri |
|
89 |
88 26
|
sstri |
|
90 |
85 89
|
eqsstri |
|
91 |
90
|
sseli |
|
92 |
91
|
imim1i |
|
93 |
92
|
6ralimi |
|
94 |
1 93
|
syl |
|
95 |
94 2 5
|
mulsproplem10 |
|
96 |
95
|
simp1d |
|
97 |
19
|
uneq2i |
|
98 |
|
un0 |
|
99 |
97 98
|
eqtri |
|
100 |
|
ssun2 |
|
101 |
100 87
|
sstri |
|
102 |
101 26
|
sstri |
|
103 |
99 102
|
eqsstri |
|
104 |
103
|
sseli |
|
105 |
104
|
imim1i |
|
106 |
105
|
6ralimi |
|
107 |
1 106
|
syl |
|
108 |
107 3 4
|
mulsproplem10 |
|
109 |
108
|
simp1d |
|
110 |
96 109
|
addscomd |
|
111 |
110
|
oveq1d |
|
112 |
19
|
uneq2i |
|
113 |
|
un0 |
|
114 |
112 113
|
eqtri |
|
115 |
|
ssun1 |
|
116 |
115 24
|
sstri |
|
117 |
116 26
|
sstri |
|
118 |
114 117
|
eqsstri |
|
119 |
118
|
sseli |
|
120 |
119
|
imim1i |
|
121 |
120
|
6ralimi |
|
122 |
1 121
|
syl |
|
123 |
122 2 4
|
mulsproplem10 |
|
124 |
123
|
simp1d |
|
125 |
109 96 124
|
addsubsassd |
|
126 |
111 125
|
eqtrd |
|
127 |
126
|
breq1d |
|
128 |
96 124
|
subscld |
|
129 |
33
|
simp1d |
|
130 |
109 128 129
|
sltaddsub2d |
|
131 |
127 130
|
bitrd |
|
132 |
131
|
adantr |
|
133 |
82 132
|
mpbid |
|
134 |
133
|
anassrs |
|
135 |
108
|
simp3d |
|
136 |
135
|
adantr |
|
137 |
|
ovex |
|
138 |
137
|
snid |
|
139 |
138
|
a1i |
|
140 |
|
simprl |
|
141 |
2
|
adantr |
|
142 |
37 141 39
|
sylancr |
|
143 |
140 142
|
mpbird |
|
144 |
6
|
adantr |
|
145 |
143 144 45
|
sylanbrc |
|
146 |
|
simprr |
|
147 |
|
bdayelon |
|
148 |
5
|
adantr |
|
149 |
|
oldbday |
|
150 |
147 148 149
|
sylancr |
|
151 |
146 150
|
mpbird |
|
152 |
7
|
adantr |
|
153 |
|
breq2 |
|
154 |
|
rightval |
|
155 |
153 154
|
elrab2 |
|
156 |
151 152 155
|
sylanbrc |
|
157 |
|
eqid |
|
158 |
|
oveq1 |
|
159 |
158
|
oveq1d |
|
160 |
|
oveq1 |
|
161 |
159 160
|
oveq12d |
|
162 |
161
|
eqeq2d |
|
163 |
|
oveq2 |
|
164 |
163
|
oveq2d |
|
165 |
|
oveq2 |
|
166 |
164 165
|
oveq12d |
|
167 |
166
|
eqeq2d |
|
168 |
162 167
|
rspc2ev |
|
169 |
157 168
|
mp3an3 |
|
170 |
145 156 169
|
syl2anc |
|
171 |
|
ovex |
|
172 |
|
eqeq1 |
|
173 |
172
|
2rexbidv |
|
174 |
171 173
|
elab |
|
175 |
170 174
|
sylibr |
|
176 |
|
elun1 |
|
177 |
175 176
|
syl |
|
178 |
136 139 177
|
ssltsepcd |
|
179 |
124 129
|
addscomd |
|
180 |
179
|
oveq1d |
|
181 |
129 124 96
|
addsubsassd |
|
182 |
180 181
|
eqtrd |
|
183 |
182
|
breq2d |
|
184 |
124 96
|
subscld |
|
185 |
109 129 184
|
sltsubadd2d |
|
186 |
183 185
|
bitr4d |
|
187 |
109 129 124 96
|
sltsubsub2bd |
|
188 |
186 187
|
bitrd |
|
189 |
188
|
adantr |
|
190 |
178 189
|
mpbid |
|
191 |
190
|
anassrs |
|
192 |
9
|
adantr |
|
193 |
134 191 192
|
mpjaodan |
|
194 |
95
|
simp3d |
|
195 |
194
|
adantr |
|
196 |
|
ovex |
|
197 |
196
|
snid |
|
198 |
197
|
a1i |
|
199 |
|
simprl |
|
200 |
|
bdayelon |
|
201 |
3
|
adantr |
|
202 |
|
oldbday |
|
203 |
200 201 202
|
sylancr |
|
204 |
199 203
|
mpbird |
|
205 |
6
|
adantr |
|
206 |
|
breq2 |
|
207 |
|
rightval |
|
208 |
206 207
|
elrab2 |
|
209 |
204 205 208
|
sylanbrc |
|
210 |
|
simprr |
|
211 |
4
|
adantr |
|
212 |
48 211 50
|
sylancr |
|
213 |
210 212
|
mpbird |
|
214 |
7
|
adantr |
|
215 |
213 214 56
|
sylanbrc |
|
216 |
|
eqid |
|
217 |
|
oveq1 |
|
218 |
217
|
oveq1d |
|
219 |
|
oveq1 |
|
220 |
218 219
|
oveq12d |
|
221 |
220
|
eqeq2d |
|
222 |
|
oveq2 |
|
223 |
222
|
oveq2d |
|
224 |
|
oveq2 |
|
225 |
223 224
|
oveq12d |
|
226 |
225
|
eqeq2d |
|
227 |
221 226
|
rspc2ev |
|
228 |
216 227
|
mp3an3 |
|
229 |
209 215 228
|
syl2anc |
|
230 |
|
ovex |
|
231 |
|
eqeq1 |
|
232 |
231
|
2rexbidv |
|
233 |
230 232
|
elab |
|
234 |
229 233
|
sylibr |
|
235 |
|
elun2 |
|
236 |
234 235
|
syl |
|
237 |
195 198 236
|
ssltsepcd |
|
238 |
129 124
|
addscomd |
|
239 |
238
|
oveq1d |
|
240 |
124 129 109
|
addsubsassd |
|
241 |
239 240
|
eqtrd |
|
242 |
241
|
breq2d |
|
243 |
129 109
|
subscld |
|
244 |
96 124 243
|
sltsubadd2d |
|
245 |
242 244
|
bitr4d |
|
246 |
245
|
adantr |
|
247 |
237 246
|
mpbid |
|
248 |
247
|
anassrs |
|
249 |
123
|
simp2d |
|
250 |
249
|
adantr |
|
251 |
|
simprl |
|
252 |
3
|
adantr |
|
253 |
200 252 202
|
sylancr |
|
254 |
251 253
|
mpbird |
|
255 |
6
|
adantr |
|
256 |
254 255 208
|
sylanbrc |
|
257 |
|
simprr |
|
258 |
5
|
adantr |
|
259 |
147 258 149
|
sylancr |
|
260 |
257 259
|
mpbird |
|
261 |
7
|
adantr |
|
262 |
260 261 155
|
sylanbrc |
|
263 |
|
eqid |
|
264 |
|
oveq1 |
|
265 |
264
|
oveq1d |
|
266 |
|
oveq1 |
|
267 |
265 266
|
oveq12d |
|
268 |
267
|
eqeq2d |
|
269 |
|
oveq2 |
|
270 |
269
|
oveq2d |
|
271 |
|
oveq2 |
|
272 |
270 271
|
oveq12d |
|
273 |
272
|
eqeq2d |
|
274 |
268 273
|
rspc2ev |
|
275 |
263 274
|
mp3an3 |
|
276 |
256 262 275
|
syl2anc |
|
277 |
|
ovex |
|
278 |
|
eqeq1 |
|
279 |
278
|
2rexbidv |
|
280 |
277 279
|
elab |
|
281 |
276 280
|
sylibr |
|
282 |
|
elun2 |
|
283 |
281 282
|
syl |
|
284 |
|
ovex |
|
285 |
284
|
snid |
|
286 |
285
|
a1i |
|
287 |
250 283 286
|
ssltsepcd |
|
288 |
109 96
|
addscomd |
|
289 |
288
|
oveq1d |
|
290 |
96 109 129
|
addsubsassd |
|
291 |
289 290
|
eqtrd |
|
292 |
291
|
breq1d |
|
293 |
109 129
|
subscld |
|
294 |
96 293 124
|
sltaddsub2d |
|
295 |
292 294
|
bitrd |
|
296 |
295 187
|
bitrd |
|
297 |
296
|
adantr |
|
298 |
287 297
|
mpbid |
|
299 |
298
|
anassrs |
|
300 |
9
|
adantr |
|
301 |
248 299 300
|
mpjaodan |
|
302 |
193 301 8
|
mpjaodan |
|