Step |
Hyp |
Ref |
Expression |
1 |
|
mulsproplem.1 |
|
2 |
|
mulsproplem8.1 |
|
3 |
|
mulsproplem8.2 |
|
4 |
|
mulsproplem8.3 |
|
5 |
|
mulsproplem8.4 |
|
6 |
|
mulsproplem8.5 |
|
7 |
|
mulsproplem8.6 |
|
8 |
|
rightssno |
|
9 |
8 4
|
sselid |
|
10 |
8 6
|
sselid |
|
11 |
|
sltlin |
|
12 |
9 10 11
|
syl2anc |
|
13 |
|
rightssold |
|
14 |
13 4
|
sselid |
|
15 |
1 14 3
|
mulsproplem2 |
|
16 |
|
rightssold |
|
17 |
16 5
|
sselid |
|
18 |
1 2 17
|
mulsproplem3 |
|
19 |
15 18
|
addscld |
|
20 |
1 14 17
|
mulsproplem4 |
|
21 |
19 20
|
subscld |
|
22 |
21
|
adantr |
|
23 |
|
leftssold |
|
24 |
23 7
|
sselid |
|
25 |
1 2 24
|
mulsproplem3 |
|
26 |
15 25
|
addscld |
|
27 |
1 14 24
|
mulsproplem4 |
|
28 |
26 27
|
subscld |
|
29 |
28
|
adantr |
|
30 |
13 6
|
sselid |
|
31 |
1 30 3
|
mulsproplem2 |
|
32 |
31 25
|
addscld |
|
33 |
1 30 24
|
mulsproplem4 |
|
34 |
32 33
|
subscld |
|
35 |
34
|
adantr |
|
36 |
|
ssltright |
|
37 |
2 36
|
syl |
|
38 |
|
snidg |
|
39 |
2 38
|
syl |
|
40 |
37 39 4
|
ssltsepcd |
|
41 |
|
lltropt |
|
42 |
41
|
a1i |
|
43 |
42 7 5
|
ssltsepcd |
|
44 |
|
0sno |
|
45 |
44
|
a1i |
|
46 |
|
leftssno |
|
47 |
46 7
|
sselid |
|
48 |
|
rightssno |
|
49 |
48 5
|
sselid |
|
50 |
|
bday0s |
|
51 |
50 50
|
oveq12i |
|
52 |
|
0elon |
|
53 |
|
naddrid |
|
54 |
52 53
|
ax-mp |
|
55 |
51 54
|
eqtri |
|
56 |
55
|
uneq1i |
|
57 |
|
0un |
|
58 |
56 57
|
eqtri |
|
59 |
|
oldbdayim |
|
60 |
24 59
|
syl |
|
61 |
|
bdayelon |
|
62 |
|
bdayelon |
|
63 |
|
bdayelon |
|
64 |
|
naddel2 |
|
65 |
61 62 63 64
|
mp3an |
|
66 |
60 65
|
sylib |
|
67 |
|
oldbdayim |
|
68 |
14 67
|
syl |
|
69 |
|
oldbdayim |
|
70 |
17 69
|
syl |
|
71 |
|
naddel12 |
|
72 |
63 62 71
|
mp2an |
|
73 |
68 70 72
|
syl2anc |
|
74 |
66 73
|
jca |
|
75 |
|
bdayelon |
|
76 |
|
naddel2 |
|
77 |
75 62 63 76
|
mp3an |
|
78 |
70 77
|
sylib |
|
79 |
|
naddel12 |
|
80 |
63 62 79
|
mp2an |
|
81 |
68 60 80
|
syl2anc |
|
82 |
78 81
|
jca |
|
83 |
|
naddcl |
|
84 |
63 61 83
|
mp2an |
|
85 |
|
bdayelon |
|
86 |
|
naddcl |
|
87 |
85 75 86
|
mp2an |
|
88 |
84 87
|
onun2i |
|
89 |
|
naddcl |
|
90 |
63 75 89
|
mp2an |
|
91 |
|
naddcl |
|
92 |
85 61 91
|
mp2an |
|
93 |
90 92
|
onun2i |
|
94 |
|
naddcl |
|
95 |
63 62 94
|
mp2an |
|
96 |
|
onunel |
|
97 |
88 93 95 96
|
mp3an |
|
98 |
|
onunel |
|
99 |
84 87 95 98
|
mp3an |
|
100 |
|
onunel |
|
101 |
90 92 95 100
|
mp3an |
|
102 |
99 101
|
anbi12i |
|
103 |
97 102
|
bitri |
|
104 |
74 82 103
|
sylanbrc |
|
105 |
|
elun1 |
|
106 |
104 105
|
syl |
|
107 |
58 106
|
eqeltrid |
|
108 |
1 45 45 2 9 47 49 107
|
mulsproplem1 |
|
109 |
108
|
simprd |
|
110 |
40 43 109
|
mp2and |
|
111 |
18 20 25 27
|
sltsubsubbd |
|
112 |
18 20
|
subscld |
|
113 |
25 27
|
subscld |
|
114 |
112 113 15
|
sltadd2d |
|
115 |
111 114
|
bitrd |
|
116 |
110 115
|
mpbid |
|
117 |
15 18 20
|
addsubsassd |
|
118 |
15 25 27
|
addsubsassd |
|
119 |
116 117 118
|
3brtr4d |
|
120 |
119
|
adantr |
|
121 |
|
ssltleft |
|
122 |
3 121
|
syl |
|
123 |
|
snidg |
|
124 |
3 123
|
syl |
|
125 |
122 7 124
|
ssltsepcd |
|
126 |
55
|
uneq1i |
|
127 |
|
0un |
|
128 |
126 127
|
eqtri |
|
129 |
|
oldbdayim |
|
130 |
30 129
|
syl |
|
131 |
|
bdayelon |
|
132 |
|
naddel1 |
|
133 |
131 63 62 132
|
mp3an |
|
134 |
130 133
|
sylib |
|
135 |
81 134
|
jca |
|
136 |
|
naddel1 |
|
137 |
85 63 62 136
|
mp3an |
|
138 |
68 137
|
sylib |
|
139 |
|
naddel12 |
|
140 |
63 62 139
|
mp2an |
|
141 |
130 60 140
|
syl2anc |
|
142 |
138 141
|
jca |
|
143 |
|
naddcl |
|
144 |
131 62 143
|
mp2an |
|
145 |
92 144
|
onun2i |
|
146 |
|
naddcl |
|
147 |
85 62 146
|
mp2an |
|
148 |
|
naddcl |
|
149 |
131 61 148
|
mp2an |
|
150 |
147 149
|
onun2i |
|
151 |
|
onunel |
|
152 |
145 150 95 151
|
mp3an |
|
153 |
|
onunel |
|
154 |
92 144 95 153
|
mp3an |
|
155 |
|
onunel |
|
156 |
147 149 95 155
|
mp3an |
|
157 |
154 156
|
anbi12i |
|
158 |
152 157
|
bitri |
|
159 |
135 142 158
|
sylanbrc |
|
160 |
|
elun1 |
|
161 |
159 160
|
syl |
|
162 |
128 161
|
eqeltrid |
|
163 |
1 45 45 9 10 47 3 162
|
mulsproplem1 |
|
164 |
163
|
simprd |
|
165 |
125 164
|
mpan2d |
|
166 |
165
|
imp |
|
167 |
15 27
|
subscld |
|
168 |
31 33
|
subscld |
|
169 |
167 168 25
|
sltadd1d |
|
170 |
169
|
adantr |
|
171 |
166 170
|
mpbid |
|
172 |
15 25 27
|
addsubsd |
|
173 |
172
|
adantr |
|
174 |
31 25 33
|
addsubsd |
|
175 |
174
|
adantr |
|
176 |
171 173 175
|
3brtr4d |
|
177 |
22 29 35 120 176
|
slttrd |
|
178 |
177
|
ex |
|
179 |
37 39 6
|
ssltsepcd |
|
180 |
55
|
uneq1i |
|
181 |
|
0un |
|
182 |
180 181
|
eqtri |
|
183 |
|
naddel12 |
|
184 |
63 62 183
|
mp2an |
|
185 |
130 70 184
|
syl2anc |
|
186 |
66 185
|
jca |
|
187 |
78 141
|
jca |
|
188 |
|
naddcl |
|
189 |
131 75 188
|
mp2an |
|
190 |
84 189
|
onun2i |
|
191 |
90 149
|
onun2i |
|
192 |
|
onunel |
|
193 |
190 191 95 192
|
mp3an |
|
194 |
|
onunel |
|
195 |
84 189 95 194
|
mp3an |
|
196 |
|
onunel |
|
197 |
90 149 95 196
|
mp3an |
|
198 |
195 197
|
anbi12i |
|
199 |
193 198
|
bitri |
|
200 |
186 187 199
|
sylanbrc |
|
201 |
|
elun1 |
|
202 |
200 201
|
syl |
|
203 |
182 202
|
eqeltrid |
|
204 |
1 45 45 2 10 47 49 203
|
mulsproplem1 |
|
205 |
204
|
simprd |
|
206 |
179 43 205
|
mp2and |
|
207 |
1 30 17
|
mulsproplem4 |
|
208 |
18 207 25 33
|
sltsubsubbd |
|
209 |
18 207
|
subscld |
|
210 |
25 33
|
subscld |
|
211 |
209 210 31
|
sltadd2d |
|
212 |
208 211
|
bitrd |
|
213 |
206 212
|
mpbid |
|
214 |
31 18 207
|
addsubsassd |
|
215 |
31 25 33
|
addsubsassd |
|
216 |
213 214 215
|
3brtr4d |
|
217 |
|
oveq1 |
|
218 |
217
|
oveq1d |
|
219 |
|
oveq1 |
|
220 |
218 219
|
oveq12d |
|
221 |
220
|
breq1d |
|
222 |
216 221
|
syl5ibrcom |
|
223 |
21
|
adantr |
|
224 |
31 18
|
addscld |
|
225 |
224 207
|
subscld |
|
226 |
225
|
adantr |
|
227 |
34
|
adantr |
|
228 |
|
ssltright |
|
229 |
3 228
|
syl |
|
230 |
229 124 5
|
ssltsepcd |
|
231 |
55
|
uneq1i |
|
232 |
|
0un |
|
233 |
231 232
|
eqtri |
|
234 |
134 73
|
jca |
|
235 |
185 138
|
jca |
|
236 |
144 87
|
onun2i |
|
237 |
189 147
|
onun2i |
|
238 |
|
onunel |
|
239 |
236 237 95 238
|
mp3an |
|
240 |
|
onunel |
|
241 |
144 87 95 240
|
mp3an |
|
242 |
|
onunel |
|
243 |
189 147 95 242
|
mp3an |
|
244 |
241 243
|
anbi12i |
|
245 |
239 244
|
bitri |
|
246 |
234 235 245
|
sylanbrc |
|
247 |
|
elun1 |
|
248 |
246 247
|
syl |
|
249 |
233 248
|
eqeltrid |
|
250 |
1 45 45 10 9 3 49 249
|
mulsproplem1 |
|
251 |
250
|
simprd |
|
252 |
230 251
|
mpan2d |
|
253 |
252
|
imp |
|
254 |
207 31 20 15
|
sltsubsub2bd |
|
255 |
15 20
|
subscld |
|
256 |
31 207
|
subscld |
|
257 |
255 256 18
|
sltadd1d |
|
258 |
254 257
|
bitrd |
|
259 |
258
|
adantr |
|
260 |
253 259
|
mpbid |
|
261 |
15 18 20
|
addsubsd |
|
262 |
261
|
adantr |
|
263 |
31 18 207
|
addsubsd |
|
264 |
263
|
adantr |
|
265 |
260 262 264
|
3brtr4d |
|
266 |
216
|
adantr |
|
267 |
223 226 227 265 266
|
slttrd |
|
268 |
267
|
ex |
|
269 |
178 222 268
|
3jaod |
|
270 |
12 269
|
mpd |
|