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 |
|
mulsproplem13.1 |
|
9 |
1
|
adantr |
|
10 |
2
|
adantr |
|
11 |
3
|
adantr |
|
12 |
4
|
adantr |
|
13 |
5
|
adantr |
|
14 |
6
|
adantr |
|
15 |
7
|
adantr |
|
16 |
|
simpr |
|
17 |
8
|
adantr |
|
18 |
9 10 11 12 13 14 15 16 17
|
mulsproplem12 |
|
19 |
2
|
adantr |
|
20 |
3
|
adantr |
|
21 |
|
simpr |
|
22 |
6
|
adantr |
|
23 |
|
nodense |
|
24 |
19 20 21 22 23
|
syl22anc |
|
25 |
|
unidm |
|
26 |
|
unidm |
|
27 |
|
bday0s |
|
28 |
27 27
|
oveq12i |
|
29 |
|
0elon |
|
30 |
|
naddrid |
|
31 |
29 30
|
ax-mp |
|
32 |
28 31
|
eqtri |
|
33 |
25 26 32
|
3eqtri |
|
34 |
33
|
uneq2i |
|
35 |
|
un0 |
|
36 |
34 35
|
eqtri |
|
37 |
|
ssun1 |
|
38 |
|
ssun2 |
|
39 |
37 38
|
sstri |
|
40 |
|
ssun2 |
|
41 |
39 40
|
sstri |
|
42 |
36 41
|
eqsstri |
|
43 |
42
|
sseli |
|
44 |
43
|
imim1i |
|
45 |
44
|
6ralimi |
|
46 |
1 45
|
syl |
|
47 |
46 2 5
|
mulsproplem11 |
|
48 |
33
|
uneq2i |
|
49 |
|
un0 |
|
50 |
48 49
|
eqtri |
|
51 |
|
ssun1 |
|
52 |
|
ssun1 |
|
53 |
51 52
|
sstri |
|
54 |
53 40
|
sstri |
|
55 |
50 54
|
eqsstri |
|
56 |
55
|
sseli |
|
57 |
56
|
imim1i |
|
58 |
57
|
6ralimi |
|
59 |
1 58
|
syl |
|
60 |
59 2 4
|
mulsproplem11 |
|
61 |
47 60
|
subscld |
|
62 |
61
|
adantr |
|
63 |
46
|
adantr |
|
64 |
|
simprr1 |
|
65 |
64
|
adantl |
|
66 |
|
bdayelon |
|
67 |
|
simprrl |
|
68 |
|
oldbday |
|
69 |
66 67 68
|
sylancr |
|
70 |
65 69
|
mpbird |
|
71 |
5
|
adantr |
|
72 |
63 70 71
|
mulsproplem2 |
|
73 |
59
|
adantr |
|
74 |
4
|
adantr |
|
75 |
73 70 74
|
mulsproplem2 |
|
76 |
72 75
|
subscld |
|
77 |
33
|
uneq2i |
|
78 |
|
un0 |
|
79 |
77 78
|
eqtri |
|
80 |
|
ssun2 |
|
81 |
80 52
|
sstri |
|
82 |
81 40
|
sstri |
|
83 |
79 82
|
eqsstri |
|
84 |
83
|
sseli |
|
85 |
84
|
imim1i |
|
86 |
85
|
6ralimi |
|
87 |
1 86
|
syl |
|
88 |
87 3 5
|
mulsproplem11 |
|
89 |
33
|
uneq2i |
|
90 |
|
un0 |
|
91 |
89 90
|
eqtri |
|
92 |
|
ssun2 |
|
93 |
92 38
|
sstri |
|
94 |
93 40
|
sstri |
|
95 |
91 94
|
eqsstri |
|
96 |
95
|
sseli |
|
97 |
96
|
imim1i |
|
98 |
97
|
6ralimi |
|
99 |
1 98
|
syl |
|
100 |
99 3 4
|
mulsproplem11 |
|
101 |
88 100
|
subscld |
|
102 |
101
|
adantr |
|
103 |
1
|
mulsproplemcbv |
|
104 |
103
|
adantr |
|
105 |
|
onelss |
|
106 |
66 65 105
|
mpsyl |
|
107 |
|
simprl |
|
108 |
106 107
|
sseqtrd |
|
109 |
|
bdayelon |
|
110 |
|
bdayelon |
|
111 |
|
bdayelon |
|
112 |
|
naddss1 |
|
113 |
109 110 111 112
|
mp3an |
|
114 |
108 113
|
sylib |
|
115 |
|
unss2 |
|
116 |
114 115
|
syl |
|
117 |
|
bdayelon |
|
118 |
|
naddss1 |
|
119 |
109 110 117 118
|
mp3an |
|
120 |
108 119
|
sylib |
|
121 |
|
unss2 |
|
122 |
120 121
|
syl |
|
123 |
|
unss12 |
|
124 |
116 122 123
|
syl2anc |
|
125 |
|
unss2 |
|
126 |
124 125
|
syl |
|
127 |
126
|
sseld |
|
128 |
127
|
imim1d |
|
129 |
128
|
ralimd6v |
|
130 |
104 129
|
mpd |
|
131 |
2
|
adantr |
|
132 |
|
simprr2 |
|
133 |
132
|
adantl |
|
134 |
7
|
adantr |
|
135 |
65
|
olcd |
|
136 |
8
|
adantr |
|
137 |
130 131 67 74 71 133 134 135 136
|
mulsproplem12 |
|
138 |
|
naddss1 |
|
139 |
109 66 117 138
|
mp3an |
|
140 |
106 139
|
sylib |
|
141 |
|
unss1 |
|
142 |
140 141
|
syl |
|
143 |
|
naddss1 |
|
144 |
109 66 111 143
|
mp3an |
|
145 |
106 144
|
sylib |
|
146 |
|
unss1 |
|
147 |
145 146
|
syl |
|
148 |
|
unss12 |
|
149 |
142 147 148
|
syl2anc |
|
150 |
|
unss2 |
|
151 |
149 150
|
syl |
|
152 |
151
|
sseld |
|
153 |
152
|
imim1d |
|
154 |
153
|
ralimd6v |
|
155 |
104 154
|
mpd |
|
156 |
3
|
adantr |
|
157 |
|
simprr3 |
|
158 |
157
|
adantl |
|
159 |
65 107
|
eleqtrd |
|
160 |
159
|
orcd |
|
161 |
155 67 156 74 71 158 134 160 136
|
mulsproplem12 |
|
162 |
62 76 102 137 161
|
slttrd |
|
163 |
162
|
anassrs |
|
164 |
24 163
|
rexlimddv |
|
165 |
66
|
onordi |
|
166 |
110
|
onordi |
|
167 |
|
ordtri3or |
|
168 |
165 166 167
|
mp2an |
|
169 |
|
df-3or |
|
170 |
|
or32 |
|
171 |
169 170
|
bitri |
|
172 |
168 171
|
mpbi |
|
173 |
172
|
a1i |
|
174 |
18 164 173
|
mpjaodan |
|