Step |
Hyp |
Ref |
Expression |
1 |
|
mulsproplem.1 |
|
2 |
|
mulsproplem6.1 |
|
3 |
|
mulsproplem6.2 |
|
4 |
|
mulsproplem6.3 |
|
5 |
|
mulsproplem6.4 |
|
6 |
|
mulsproplem6.5 |
|
7 |
|
mulsproplem6.6 |
|
8 |
|
leftssno |
|
9 |
8 5
|
sselid |
|
10 |
8 7
|
sselid |
|
11 |
|
sltlin |
|
12 |
9 10 11
|
syl2anc |
|
13 |
|
leftssold |
|
14 |
13 4
|
sselid |
|
15 |
1 14 3
|
mulsproplem2 |
|
16 |
|
leftssold |
|
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 |
16 7
|
sselid |
|
24 |
1 2 23
|
mulsproplem3 |
|
25 |
15 24
|
addscld |
|
26 |
1 14 23
|
mulsproplem4 |
|
27 |
25 26
|
subscld |
|
28 |
27
|
adantr |
|
29 |
|
rightssold |
|
30 |
29 6
|
sselid |
|
31 |
1 30 3
|
mulsproplem2 |
|
32 |
31 24
|
addscld |
|
33 |
1 30 23
|
mulsproplem4 |
|
34 |
32 33
|
subscld |
|
35 |
34
|
adantr |
|
36 |
|
ssltleft |
|
37 |
2 36
|
syl |
|
38 |
|
snidg |
|
39 |
2 38
|
syl |
|
40 |
37 4 39
|
ssltsepcd |
|
41 |
|
0sno |
|
42 |
41
|
a1i |
|
43 |
|
leftssno |
|
44 |
43 4
|
sselid |
|
45 |
|
bday0s |
|
46 |
45 45
|
oveq12i |
|
47 |
|
0elon |
|
48 |
|
naddrid |
|
49 |
47 48
|
ax-mp |
|
50 |
46 49
|
eqtri |
|
51 |
50
|
uneq1i |
|
52 |
|
0un |
|
53 |
51 52
|
eqtri |
|
54 |
|
oldbdayim |
|
55 |
14 54
|
syl |
|
56 |
|
oldbdayim |
|
57 |
17 56
|
syl |
|
58 |
|
bdayelon |
|
59 |
|
bdayelon |
|
60 |
|
naddel12 |
|
61 |
58 59 60
|
mp2an |
|
62 |
55 57 61
|
syl2anc |
|
63 |
|
oldbdayim |
|
64 |
23 63
|
syl |
|
65 |
|
bdayelon |
|
66 |
|
naddel2 |
|
67 |
65 59 58 66
|
mp3an |
|
68 |
64 67
|
sylib |
|
69 |
62 68
|
jca |
|
70 |
|
naddel12 |
|
71 |
58 59 70
|
mp2an |
|
72 |
55 64 71
|
syl2anc |
|
73 |
|
bdayelon |
|
74 |
|
naddel2 |
|
75 |
73 59 58 74
|
mp3an |
|
76 |
57 75
|
sylib |
|
77 |
72 76
|
jca |
|
78 |
|
bdayelon |
|
79 |
|
naddcl |
|
80 |
78 73 79
|
mp2an |
|
81 |
|
naddcl |
|
82 |
58 65 81
|
mp2an |
|
83 |
80 82
|
onun2i |
|
84 |
|
naddcl |
|
85 |
78 65 84
|
mp2an |
|
86 |
|
naddcl |
|
87 |
58 73 86
|
mp2an |
|
88 |
85 87
|
onun2i |
|
89 |
|
naddcl |
|
90 |
58 59 89
|
mp2an |
|
91 |
|
onunel |
|
92 |
83 88 90 91
|
mp3an |
|
93 |
|
onunel |
|
94 |
80 82 90 93
|
mp3an |
|
95 |
|
onunel |
|
96 |
85 87 90 95
|
mp3an |
|
97 |
94 96
|
anbi12i |
|
98 |
92 97
|
bitri |
|
99 |
69 77 98
|
sylanbrc |
|
100 |
|
elun1 |
|
101 |
99 100
|
syl |
|
102 |
53 101
|
eqeltrid |
|
103 |
1 42 42 44 2 9 10 102
|
mulsproplem1 |
|
104 |
103
|
simprd |
|
105 |
40 104
|
mpand |
|
106 |
105
|
imp |
|
107 |
26 24 20 18
|
sltsubsub3bd |
|
108 |
18 20
|
subscld |
|
109 |
24 26
|
subscld |
|
110 |
108 109 15
|
sltadd2d |
|
111 |
107 110
|
bitrd |
|
112 |
111
|
adantr |
|
113 |
106 112
|
mpbid |
|
114 |
15 18 20
|
addsubsassd |
|
115 |
114
|
adantr |
|
116 |
15 24 26
|
addsubsassd |
|
117 |
116
|
adantr |
|
118 |
113 115 117
|
3brtr4d |
|
119 |
|
lltropt |
|
120 |
119
|
a1i |
|
121 |
120 4 6
|
ssltsepcd |
|
122 |
|
ssltleft |
|
123 |
3 122
|
syl |
|
124 |
|
snidg |
|
125 |
3 124
|
syl |
|
126 |
123 7 125
|
ssltsepcd |
|
127 |
|
rightssno |
|
128 |
127 6
|
sselid |
|
129 |
50
|
uneq1i |
|
130 |
|
0un |
|
131 |
129 130
|
eqtri |
|
132 |
|
oldbdayim |
|
133 |
30 132
|
syl |
|
134 |
|
bdayelon |
|
135 |
|
naddel1 |
|
136 |
134 58 59 135
|
mp3an |
|
137 |
133 136
|
sylib |
|
138 |
72 137
|
jca |
|
139 |
|
naddel1 |
|
140 |
78 58 59 139
|
mp3an |
|
141 |
55 140
|
sylib |
|
142 |
|
naddel12 |
|
143 |
58 59 142
|
mp2an |
|
144 |
133 64 143
|
syl2anc |
|
145 |
141 144
|
jca |
|
146 |
|
naddcl |
|
147 |
134 59 146
|
mp2an |
|
148 |
85 147
|
onun2i |
|
149 |
|
naddcl |
|
150 |
78 59 149
|
mp2an |
|
151 |
|
naddcl |
|
152 |
134 65 151
|
mp2an |
|
153 |
150 152
|
onun2i |
|
154 |
|
onunel |
|
155 |
148 153 90 154
|
mp3an |
|
156 |
|
onunel |
|
157 |
85 147 90 156
|
mp3an |
|
158 |
|
onunel |
|
159 |
150 152 90 158
|
mp3an |
|
160 |
157 159
|
anbi12i |
|
161 |
155 160
|
bitri |
|
162 |
138 145 161
|
sylanbrc |
|
163 |
|
elun1 |
|
164 |
162 163
|
syl |
|
165 |
131 164
|
eqeltrid |
|
166 |
1 42 42 44 128 10 3 165
|
mulsproplem1 |
|
167 |
166
|
simprd |
|
168 |
121 126 167
|
mp2and |
|
169 |
15 26
|
subscld |
|
170 |
31 33
|
subscld |
|
171 |
169 170 24
|
sltadd1d |
|
172 |
168 171
|
mpbid |
|
173 |
15 24 26
|
addsubsd |
|
174 |
31 24 33
|
addsubsd |
|
175 |
172 173 174
|
3brtr4d |
|
176 |
175
|
adantr |
|
177 |
22 28 35 118 176
|
slttrd |
|
178 |
177
|
ex |
|
179 |
|
oveq2 |
|
180 |
179
|
oveq2d |
|
181 |
|
oveq2 |
|
182 |
180 181
|
oveq12d |
|
183 |
182
|
breq1d |
|
184 |
175 183
|
syl5ibrcom |
|
185 |
21
|
adantr |
|
186 |
31 18
|
addscld |
|
187 |
1 30 17
|
mulsproplem4 |
|
188 |
186 187
|
subscld |
|
189 |
188
|
adantr |
|
190 |
34
|
adantr |
|
191 |
123 5 125
|
ssltsepcd |
|
192 |
50
|
uneq1i |
|
193 |
|
0un |
|
194 |
192 193
|
eqtri |
|
195 |
62 137
|
jca |
|
196 |
|
naddel12 |
|
197 |
58 59 196
|
mp2an |
|
198 |
133 57 197
|
syl2anc |
|
199 |
141 198
|
jca |
|
200 |
80 147
|
onun2i |
|
201 |
|
naddcl |
|
202 |
134 73 201
|
mp2an |
|
203 |
150 202
|
onun2i |
|
204 |
|
onunel |
|
205 |
200 203 90 204
|
mp3an |
|
206 |
|
onunel |
|
207 |
80 147 90 206
|
mp3an |
|
208 |
|
onunel |
|
209 |
150 202 90 208
|
mp3an |
|
210 |
207 209
|
anbi12i |
|
211 |
205 210
|
bitri |
|
212 |
195 199 211
|
sylanbrc |
|
213 |
|
elun1 |
|
214 |
212 213
|
syl |
|
215 |
194 214
|
eqeltrid |
|
216 |
1 42 42 44 128 9 3 215
|
mulsproplem1 |
|
217 |
216
|
simprd |
|
218 |
121 191 217
|
mp2and |
|
219 |
15 20
|
subscld |
|
220 |
31 187
|
subscld |
|
221 |
219 220 18
|
sltadd1d |
|
222 |
218 221
|
mpbid |
|
223 |
15 18 20
|
addsubsd |
|
224 |
31 18 187
|
addsubsd |
|
225 |
222 223 224
|
3brtr4d |
|
226 |
225
|
adantr |
|
227 |
|
ssltright |
|
228 |
2 227
|
syl |
|
229 |
228 39 6
|
ssltsepcd |
|
230 |
50
|
uneq1i |
|
231 |
|
0un |
|
232 |
230 231
|
eqtri |
|
233 |
68 198
|
jca |
|
234 |
76 144
|
jca |
|
235 |
82 202
|
onun2i |
|
236 |
87 152
|
onun2i |
|
237 |
|
onunel |
|
238 |
235 236 90 237
|
mp3an |
|
239 |
|
onunel |
|
240 |
82 202 90 239
|
mp3an |
|
241 |
|
onunel |
|
242 |
87 152 90 241
|
mp3an |
|
243 |
240 242
|
anbi12i |
|
244 |
238 243
|
bitri |
|
245 |
233 234 244
|
sylanbrc |
|
246 |
|
elun1 |
|
247 |
245 246
|
syl |
|
248 |
232 247
|
eqeltrid |
|
249 |
1 42 42 2 128 10 9 248
|
mulsproplem1 |
|
250 |
249
|
simprd |
|
251 |
229 250
|
mpand |
|
252 |
251
|
imp |
|
253 |
18 187 24 33
|
sltsubsubbd |
|
254 |
18 187
|
subscld |
|
255 |
24 33
|
subscld |
|
256 |
254 255 31
|
sltadd2d |
|
257 |
253 256
|
bitrd |
|
258 |
257
|
adantr |
|
259 |
252 258
|
mpbid |
|
260 |
31 18 187
|
addsubsassd |
|
261 |
260
|
adantr |
|
262 |
31 24 33
|
addsubsassd |
|
263 |
262
|
adantr |
|
264 |
259 261 263
|
3brtr4d |
|
265 |
185 189 190 226 264
|
slttrd |
|
266 |
265
|
ex |
|
267 |
178 184 266
|
3jaod |
|
268 |
12 267
|
mpd |
|