Step |
Hyp |
Ref |
Expression |
1 |
|
dalawlem.l |
|
2 |
|
dalawlem.j |
|
3 |
|
dalawlem.m |
|
4 |
|
dalawlem.a |
|
5 |
|
eqid |
|
6 |
|
simp11 |
|
7 |
6
|
hllatd |
|
8 |
|
simp22 |
|
9 |
|
simp32 |
|
10 |
5 2 4
|
hlatjcl |
|
11 |
6 8 9 10
|
syl3anc |
|
12 |
|
simp21 |
|
13 |
5 4
|
atbase |
|
14 |
12 13
|
syl |
|
15 |
5 2
|
latjcl |
|
16 |
7 11 14 15
|
syl3anc |
|
17 |
|
simp31 |
|
18 |
5 4
|
atbase |
|
19 |
17 18
|
syl |
|
20 |
5 3
|
latmcl |
|
21 |
7 16 19 20
|
syl3anc |
|
22 |
|
simp23 |
|
23 |
5 2 4
|
hlatjcl |
|
24 |
6 8 22 23
|
syl3anc |
|
25 |
|
simp33 |
|
26 |
5 4
|
atbase |
|
27 |
25 26
|
syl |
|
28 |
5 3
|
latmcl |
|
29 |
7 24 27 28
|
syl3anc |
|
30 |
5 2 4
|
hlatjcl |
|
31 |
6 22 12 30
|
syl3anc |
|
32 |
5 2 4
|
hlatjcl |
|
33 |
6 25 17 32
|
syl3anc |
|
34 |
5 3
|
latmcl |
|
35 |
7 31 33 34
|
syl3anc |
|
36 |
5 2
|
latjcl |
|
37 |
7 29 35 36
|
syl3anc |
|
38 |
5 2 4
|
hlatjcl |
|
39 |
6 9 25 38
|
syl3anc |
|
40 |
5 3
|
latmcl |
|
41 |
7 24 39 40
|
syl3anc |
|
42 |
5 2
|
latjcl |
|
43 |
7 41 35 42
|
syl3anc |
|
44 |
5 4
|
atbase |
|
45 |
8 44
|
syl |
|
46 |
5 3
|
latmcl |
|
47 |
7 45 27 46
|
syl3anc |
|
48 |
5 2 4
|
hlatjcl |
|
49 |
6 12 17 48
|
syl3anc |
|
50 |
5 3
|
latmcl |
|
51 |
7 49 45 50
|
syl3anc |
|
52 |
5 2
|
latjcl |
|
53 |
7 47 51 52
|
syl3anc |
|
54 |
5 2
|
latjcl |
|
55 |
7 14 53 54
|
syl3anc |
|
56 |
5 4
|
atbase |
|
57 |
22 56
|
syl |
|
58 |
5 2
|
latjcl |
|
59 |
7 57 29 58
|
syl3anc |
|
60 |
5 2
|
latjcl |
|
61 |
7 14 59 60
|
syl3anc |
|
62 |
5 2
|
latjcl |
|
63 |
7 47 14 62
|
syl3anc |
|
64 |
5 1 2 3
|
latmlej22 |
|
65 |
7 19 16 63 64
|
syl13anc |
|
66 |
5 2
|
latjass |
|
67 |
7 47 14 19 66
|
syl13anc |
|
68 |
65 67
|
breqtrd |
|
69 |
5 3
|
latmcl |
|
70 |
7 11 49 69
|
syl3anc |
|
71 |
5 2
|
latjcl |
|
72 |
7 70 14 71
|
syl3anc |
|
73 |
5 2 4
|
hlatjcl |
|
74 |
6 12 8 73
|
syl3anc |
|
75 |
1 2 4
|
hlatlej2 |
|
76 |
6 12 17 75
|
syl3anc |
|
77 |
5 1 3
|
latmlem2 |
|
78 |
7 19 49 16 77
|
syl13anc |
|
79 |
76 78
|
mpd |
|
80 |
1 2 4
|
hlatlej1 |
|
81 |
6 12 17 80
|
syl3anc |
|
82 |
5 1 2 3 4
|
atmod4i1 |
|
83 |
6 12 11 49 81 82
|
syl131anc |
|
84 |
79 83
|
breqtrrd |
|
85 |
5 3
|
latmcom |
|
86 |
7 11 49 85
|
syl3anc |
|
87 |
|
simp12 |
|
88 |
86 87
|
eqbrtrd |
|
89 |
1 2 4
|
hlatlej1 |
|
90 |
6 12 8 89
|
syl3anc |
|
91 |
5 1 2
|
latjle12 |
|
92 |
7 70 14 74 91
|
syl13anc |
|
93 |
88 90 92
|
mpbi2and |
|
94 |
5 1 7 21 72 74 84 93
|
lattrd |
|
95 |
5 2
|
latjcl |
|
96 |
7 47 49 95
|
syl3anc |
|
97 |
5 1 3
|
latlem12 |
|
98 |
7 21 96 74 97
|
syl13anc |
|
99 |
68 94 98
|
mpbi2and |
|
100 |
5 1 2 3 4
|
atmod3i1 |
|
101 |
6 12 49 45 81 100
|
syl131anc |
|
102 |
101
|
oveq2d |
|
103 |
5 2
|
latj12 |
|
104 |
7 47 14 51 103
|
syl13anc |
|
105 |
5 1 2 3
|
latmlej12 |
|
106 |
7 45 27 14 105
|
syl13anc |
|
107 |
5 1 2 3 4
|
atmod1i1m |
|
108 |
6 25 45 49 74 106 107
|
syl231anc |
|
109 |
102 104 108
|
3eqtr3rd |
|
110 |
99 109
|
breqtrd |
|
111 |
1 2 4
|
hlatlej1 |
|
112 |
6 8 22 111
|
syl3anc |
|
113 |
1 2 4
|
hlatlej2 |
|
114 |
6 22 25 113
|
syl3anc |
|
115 |
5 3
|
latmcl |
|
116 |
7 49 11 115
|
syl3anc |
|
117 |
5 2 4
|
hlatjcl |
|
118 |
6 22 25 117
|
syl3anc |
|
119 |
1 2 4
|
hlatlej1 |
|
120 |
6 8 9 119
|
syl3anc |
|
121 |
5 1 3
|
latmlem2 |
|
122 |
7 45 11 49 121
|
syl13anc |
|
123 |
120 122
|
mpd |
|
124 |
|
simp13 |
|
125 |
5 1 7 51 116 118 123 124
|
lattrd |
|
126 |
5 1 2
|
latjle12 |
|
127 |
7 27 51 118 126
|
syl13anc |
|
128 |
114 125 127
|
mpbi2and |
|
129 |
5 2
|
latjcl |
|
130 |
7 27 51 129
|
syl3anc |
|
131 |
5 1 3
|
latmlem12 |
|
132 |
7 45 24 130 118 131
|
syl122anc |
|
133 |
112 128 132
|
mp2and |
|
134 |
5 1 3
|
latmle2 |
|
135 |
7 49 45 134
|
syl3anc |
|
136 |
5 1 2 3 4
|
atmod2i2 |
|
137 |
6 25 45 51 135 136
|
syl131anc |
|
138 |
1 2 4
|
hlatlej2 |
|
139 |
6 8 22 138
|
syl3anc |
|
140 |
5 1 2 3 4
|
atmod3i2 |
|
141 |
6 25 57 24 139 140
|
syl131anc |
|
142 |
133 137 141
|
3brtr4d |
|
143 |
5 1 2
|
latjlej2 |
|
144 |
7 53 59 14 143
|
syl13anc |
|
145 |
142 144
|
mpd |
|
146 |
5 1 7 21 55 61 110 145
|
lattrd |
|
147 |
5 2
|
latj13 |
|
148 |
7 14 57 29 147
|
syl13anc |
|
149 |
146 148
|
breqtrd |
|
150 |
5 1 2 3
|
latmlej22 |
|
151 |
7 19 16 27 150
|
syl13anc |
|
152 |
5 2
|
latjcl |
|
153 |
7 29 31 152
|
syl3anc |
|
154 |
5 1 3
|
latlem12 |
|
155 |
7 21 153 33 154
|
syl13anc |
|
156 |
149 151 155
|
mpbi2and |
|
157 |
5 1 2 3
|
latmlej21 |
|
158 |
7 27 24 19 157
|
syl13anc |
|
159 |
5 1 2 3 4
|
atmod1i1m |
|
160 |
6 25 24 31 33 158 159
|
syl231anc |
|
161 |
156 160
|
breqtrrd |
|
162 |
1 2 4
|
hlatlej2 |
|
163 |
6 9 25 162
|
syl3anc |
|
164 |
5 1 3
|
latmlem2 |
|
165 |
7 27 39 24 164
|
syl13anc |
|
166 |
163 165
|
mpd |
|
167 |
5 1 2
|
latjlej1 |
|
168 |
7 29 41 35 167
|
syl13anc |
|
169 |
166 168
|
mpd |
|
170 |
5 1 7 21 37 43 161 169
|
lattrd |
|