Step |
Hyp |
Ref |
Expression |
1 |
|
mulsproplem.1 |
|
2 |
|
mulsproplem7.1 |
|
3 |
|
mulsproplem7.2 |
|
4 |
|
mulsproplem7.3 |
|
5 |
|
mulsproplem7.4 |
|
6 |
|
mulsproplem7.5 |
|
7 |
|
mulsproplem7.6 |
|
8 |
|
rightssno |
|
9 |
8 5
|
sselid |
|
10 |
8 7
|
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 6
|
sselid |
|
25 |
1 24 3
|
mulsproplem2 |
|
26 |
25 18
|
addscld |
|
27 |
1 24 17
|
mulsproplem4 |
|
28 |
26 27
|
subscld |
|
29 |
28
|
adantr |
|
30 |
16 7
|
sselid |
|
31 |
1 2 30
|
mulsproplem3 |
|
32 |
25 31
|
addscld |
|
33 |
1 24 30
|
mulsproplem4 |
|
34 |
32 33
|
subscld |
|
35 |
34
|
adantr |
|
36 |
|
lltropt |
|
37 |
36
|
a1i |
|
38 |
37 6 4
|
ssltsepcd |
|
39 |
|
ssltright |
|
40 |
3 39
|
syl |
|
41 |
|
snidg |
|
42 |
3 41
|
syl |
|
43 |
40 42 5
|
ssltsepcd |
|
44 |
|
0sno |
|
45 |
44
|
a1i |
|
46 |
|
leftssno |
|
47 |
46 6
|
sselid |
|
48 |
|
rightssno |
|
49 |
48 4
|
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 |
|
naddel1 |
|
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 |
62 63 71
|
mp2an |
|
73 |
68 70 72
|
syl2anc |
|
74 |
66 73
|
jca |
|
75 |
|
naddel12 |
|
76 |
62 63 75
|
mp2an |
|
77 |
60 70 76
|
syl2anc |
|
78 |
|
bdayelon |
|
79 |
|
naddel1 |
|
80 |
78 62 63 79
|
mp3an |
|
81 |
68 80
|
sylib |
|
82 |
77 81
|
jca |
|
83 |
|
naddcl |
|
84 |
61 63 83
|
mp2an |
|
85 |
|
bdayelon |
|
86 |
|
naddcl |
|
87 |
78 85 86
|
mp2an |
|
88 |
84 87
|
onun2i |
|
89 |
|
naddcl |
|
90 |
61 85 89
|
mp2an |
|
91 |
|
naddcl |
|
92 |
78 63 91
|
mp2an |
|
93 |
90 92
|
onun2i |
|
94 |
|
naddcl |
|
95 |
62 63 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 47 49 3 9 107
|
mulsproplem1 |
|
109 |
108
|
simprd |
|
110 |
38 43 109
|
mp2and |
|
111 |
27 25 20 15
|
sltsubsub2bd |
|
112 |
15 20
|
subscld |
|
113 |
25 27
|
subscld |
|
114 |
112 113 18
|
sltadd1d |
|
115 |
111 114
|
bitrd |
|
116 |
110 115
|
mpbid |
|
117 |
15 18 20
|
addsubsd |
|
118 |
25 18 27
|
addsubsd |
|
119 |
116 117 118
|
3brtr4d |
|
120 |
119
|
adantr |
|
121 |
|
ssltleft |
|
122 |
2 121
|
syl |
|
123 |
|
snidg |
|
124 |
2 123
|
syl |
|
125 |
122 6 124
|
ssltsepcd |
|
126 |
55
|
uneq1i |
|
127 |
|
0un |
|
128 |
126 127
|
eqtri |
|
129 |
|
oldbdayim |
|
130 |
30 129
|
syl |
|
131 |
|
bdayelon |
|
132 |
|
naddel2 |
|
133 |
131 63 62 132
|
mp3an |
|
134 |
130 133
|
sylib |
|
135 |
77 134
|
jca |
|
136 |
|
naddel12 |
|
137 |
62 63 136
|
mp2an |
|
138 |
60 130 137
|
syl2anc |
|
139 |
|
naddel2 |
|
140 |
85 63 62 139
|
mp3an |
|
141 |
70 140
|
sylib |
|
142 |
138 141
|
jca |
|
143 |
|
naddcl |
|
144 |
62 131 143
|
mp2an |
|
145 |
90 144
|
onun2i |
|
146 |
|
naddcl |
|
147 |
61 131 146
|
mp2an |
|
148 |
|
naddcl |
|
149 |
62 85 148
|
mp2an |
|
150 |
147 149
|
onun2i |
|
151 |
|
onunel |
|
152 |
145 150 95 151
|
mp3an |
|
153 |
|
onunel |
|
154 |
90 144 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 47 2 9 10 162
|
mulsproplem1 |
|
164 |
163
|
simprd |
|
165 |
125 164
|
mpand |
|
166 |
165
|
imp |
|
167 |
33 31 27 18
|
sltsubsub3bd |
|
168 |
18 27
|
subscld |
|
169 |
31 33
|
subscld |
|
170 |
168 169 25
|
sltadd2d |
|
171 |
167 170
|
bitrd |
|
172 |
171
|
adantr |
|
173 |
166 172
|
mpbid |
|
174 |
25 18 27
|
addsubsassd |
|
175 |
174
|
adantr |
|
176 |
25 31 33
|
addsubsassd |
|
177 |
176
|
adantr |
|
178 |
173 175 177
|
3brtr4d |
|
179 |
22 29 35 120 178
|
slttrd |
|
180 |
179
|
ex |
|
181 |
40 42 7
|
ssltsepcd |
|
182 |
55
|
uneq1i |
|
183 |
|
0un |
|
184 |
182 183
|
eqtri |
|
185 |
|
naddel12 |
|
186 |
62 63 185
|
mp2an |
|
187 |
68 130 186
|
syl2anc |
|
188 |
66 187
|
jca |
|
189 |
138 81
|
jca |
|
190 |
|
naddcl |
|
191 |
78 131 190
|
mp2an |
|
192 |
84 191
|
onun2i |
|
193 |
147 92
|
onun2i |
|
194 |
|
onunel |
|
195 |
192 193 95 194
|
mp3an |
|
196 |
|
onunel |
|
197 |
84 191 95 196
|
mp3an |
|
198 |
|
onunel |
|
199 |
147 92 95 198
|
mp3an |
|
200 |
197 199
|
anbi12i |
|
201 |
195 200
|
bitri |
|
202 |
188 189 201
|
sylanbrc |
|
203 |
|
elun1 |
|
204 |
202 203
|
syl |
|
205 |
184 204
|
eqeltrid |
|
206 |
1 45 45 47 49 3 10 205
|
mulsproplem1 |
|
207 |
206
|
simprd |
|
208 |
38 181 207
|
mp2and |
|
209 |
1 14 30
|
mulsproplem4 |
|
210 |
33 25 209 15
|
sltsubsub2bd |
|
211 |
15 209
|
subscld |
|
212 |
25 33
|
subscld |
|
213 |
211 212 31
|
sltadd1d |
|
214 |
210 213
|
bitrd |
|
215 |
208 214
|
mpbid |
|
216 |
15 31 209
|
addsubsd |
|
217 |
25 31 33
|
addsubsd |
|
218 |
215 216 217
|
3brtr4d |
|
219 |
|
oveq2 |
|
220 |
219
|
oveq2d |
|
221 |
|
oveq2 |
|
222 |
220 221
|
oveq12d |
|
223 |
222
|
breq1d |
|
224 |
218 223
|
syl5ibrcom |
|
225 |
21
|
adantr |
|
226 |
15 31
|
addscld |
|
227 |
226 209
|
subscld |
|
228 |
227
|
adantr |
|
229 |
34
|
adantr |
|
230 |
|
ssltright |
|
231 |
2 230
|
syl |
|
232 |
231 124 4
|
ssltsepcd |
|
233 |
55
|
uneq1i |
|
234 |
|
0un |
|
235 |
233 234
|
eqtri |
|
236 |
134 73
|
jca |
|
237 |
141 187
|
jca |
|
238 |
144 87
|
onun2i |
|
239 |
149 191
|
onun2i |
|
240 |
|
onunel |
|
241 |
238 239 95 240
|
mp3an |
|
242 |
|
onunel |
|
243 |
144 87 95 242
|
mp3an |
|
244 |
|
onunel |
|
245 |
149 191 95 244
|
mp3an |
|
246 |
243 245
|
anbi12i |
|
247 |
241 246
|
bitri |
|
248 |
236 237 247
|
sylanbrc |
|
249 |
|
elun1 |
|
250 |
248 249
|
syl |
|
251 |
235 250
|
eqeltrid |
|
252 |
1 45 45 2 49 10 9 251
|
mulsproplem1 |
|
253 |
252
|
simprd |
|
254 |
232 253
|
mpand |
|
255 |
254
|
imp |
|
256 |
18 20 31 209
|
sltsubsubbd |
|
257 |
18 20
|
subscld |
|
258 |
31 209
|
subscld |
|
259 |
257 258 15
|
sltadd2d |
|
260 |
256 259
|
bitrd |
|
261 |
260
|
adantr |
|
262 |
255 261
|
mpbid |
|
263 |
15 18 20
|
addsubsassd |
|
264 |
263
|
adantr |
|
265 |
15 31 209
|
addsubsassd |
|
266 |
265
|
adantr |
|
267 |
262 264 266
|
3brtr4d |
|
268 |
218
|
adantr |
|
269 |
225 228 229 267 268
|
slttrd |
|
270 |
269
|
ex |
|
271 |
180 224 270
|
3jaod |
|
272 |
12 271
|
mpd |
|