Proof of Theorem dalawlem11
Step | Hyp | Ref
| Expression |
1 | | eqid 2622 |
. . . 4
|
2 | | dalawlem.l |
. . . 4
|
3 | | simp11 1091 |
. . . . 5
|
4 | | hllat 34650 |
. . . . 5
|
5 | 3, 4 | syl 17 |
. . . 4
|
6 | | simp21 1094 |
. . . . . 6
|
7 | | simp22 1095 |
. . . . . 6
|
8 | | dalawlem.j |
. . . . . . 7
|
9 | | dalawlem.a |
. . . . . . 7
|
10 | 1, 8, 9 | hlatjcl 34653 |
. . . . . 6
|
11 | 3, 6, 7, 10 | syl3anc 1326 |
. . . . 5
|
12 | | simp31 1097 |
. . . . . 6
|
13 | | simp32 1098 |
. . . . . 6
|
14 | 1, 8, 9 | hlatjcl 34653 |
. . . . . 6
|
15 | 3, 12, 13, 14 | syl3anc 1326 |
. . . . 5
|
16 | | dalawlem.m |
. . . . . 6
|
17 | 1, 16 | latmcl 17052 |
. . . . 5
|
18 | 5, 11, 15, 17 | syl3anc 1326 |
. . . 4
|
19 | | simp23 1096 |
. . . . 5
|
20 | 1, 8, 9 | hlatjcl 34653 |
. . . . 5
|
21 | 3, 7, 19, 20 | syl3anc 1326 |
. . . 4
|
22 | 1, 2, 16 | latmle1 17076 |
. . . . 5
|
23 | 5, 11, 15, 22 | syl3anc 1326 |
. . . 4
|
24 | | simp12 1092 |
. . . . 5
|
25 | 1, 9 | atbase 34576 |
. . . . . . 7
|
26 | 7, 25 | syl 17 |
. . . . . 6
|
27 | 1, 9 | atbase 34576 |
. . . . . . 7
|
28 | 19, 27 | syl 17 |
. . . . . 6
|
29 | 1, 2, 8 | latlej1 17060 |
. . . . . 6
|
30 | 5, 26, 28, 29 | syl3anc 1326 |
. . . . 5
|
31 | 1, 9 | atbase 34576 |
. . . . . . 7
|
32 | 6, 31 | syl 17 |
. . . . . 6
|
33 | 1, 2, 8 | latjle12 17062 |
. . . . . 6
|
34 | 5, 32, 26, 21, 33 | syl13anc 1328 |
. . . . 5
|
35 | 24, 30, 34 | mpbi2and 956 |
. . . 4
|
36 | 1, 2, 5, 18, 11, 21, 23, 35 | lattrd 17058 |
. . 3
|
37 | 1, 9 | atbase 34576 |
. . . . . . . 8
|
38 | 13, 37 | syl 17 |
. . . . . . 7
|
39 | 1, 8 | latjcl 17051 |
. . . . . . 7
|
40 | 5, 11, 38, 39 | syl3anc 1326 |
. . . . . 6
|
41 | 1, 16 | latmcl 17052 |
. . . . . 6
|
42 | 5, 40, 15, 41 | syl3anc 1326 |
. . . . 5
|
43 | 1, 8, 9 | hlatjcl 34653 |
. . . . . . . . 9
|
44 | 3, 19, 6, 43 | syl3anc 1326 |
. . . . . . . 8
|
45 | | simp33 1099 |
. . . . . . . . 9
|
46 | 1, 8, 9 | hlatjcl 34653 |
. . . . . . . . 9
|
47 | 3, 45, 12, 46 | syl3anc 1326 |
. . . . . . . 8
|
48 | 1, 16 | latmcl 17052 |
. . . . . . . 8
|
49 | 5, 44, 47, 48 | syl3anc 1326 |
. . . . . . 7
|
50 | 1, 9 | atbase 34576 |
. . . . . . . 8
|
51 | 45, 50 | syl 17 |
. . . . . . 7
|
52 | 1, 8 | latjcl 17051 |
. . . . . . 7
|
53 | 5, 49, 51, 52 | syl3anc 1326 |
. . . . . 6
|
54 | 1, 8 | latjcl 17051 |
. . . . . 6
|
55 | 5, 53, 38, 54 | syl3anc 1326 |
. . . . 5
|
56 | 1, 2, 8 | latlej1 17060 |
. . . . . . 7
|
57 | 5, 11, 38, 56 | syl3anc 1326 |
. . . . . 6
|
58 | 1, 2, 16 | latmlem1 17081 |
. . . . . . 7
|
59 | 5, 11, 40, 15, 58 | syl13anc 1328 |
. . . . . 6
|
60 | 57, 59 | mpd 15 |
. . . . 5
|
61 | 1, 2, 8 | latlej2 17061 |
. . . . . . . 8
|
62 | 5, 11, 38, 61 | syl3anc 1326 |
. . . . . . 7
|
63 | 1, 2, 8, 16, 9 | atmod2i2 35148 |
. . . . . . 7
|
64 | 3, 12, 40, 38, 62, 63 | syl131anc 1339 |
. . . . . 6
|
65 | 1, 8, 9 | hlatjcl 34653 |
. . . . . . . . . . . . . 14
|
66 | 3, 7, 13, 65 | syl3anc 1326 |
. . . . . . . . . . . . 13
|
67 | 1, 8, 9 | hlatjcl 34653 |
. . . . . . . . . . . . . 14
|
68 | 3, 6, 12, 67 | syl3anc 1326 |
. . . . . . . . . . . . 13
|
69 | 1, 16 | latmcom 17075 |
. . . . . . . . . . . . 13
|
70 | 5, 66, 68, 69 | syl3anc 1326 |
. . . . . . . . . . . 12
|
71 | | simp13 1093 |
. . . . . . . . . . . 12
|
72 | 70, 71 | eqbrtrd 4675 |
. . . . . . . . . . 11
|
73 | 1, 16 | latmcl 17052 |
. . . . . . . . . . . . 13
|
74 | 5, 66, 68, 73 | syl3anc 1326 |
. . . . . . . . . . . 12
|
75 | 1, 8, 9 | hlatjcl 34653 |
. . . . . . . . . . . . 13
|
76 | 3, 19, 45, 75 | syl3anc 1326 |
. . . . . . . . . . . 12
|
77 | 1, 2, 8 | latjlej2 17066 |
. . . . . . . . . . . 12
|
78 | 5, 74, 76, 32, 77 | syl13anc 1328 |
. . . . . . . . . . 11
|
79 | 72, 78 | mpd 15 |
. . . . . . . . . 10
|
80 | 1, 9 | atbase 34576 |
. . . . . . . . . . . . 13
|
81 | 12, 80 | syl 17 |
. . . . . . . . . . . 12
|
82 | 1, 2, 8 | latlej1 17060 |
. . . . . . . . . . . 12
|
83 | 5, 32, 81, 82 | syl3anc 1326 |
. . . . . . . . . . 11
|
84 | 1, 2, 8, 16, 9 | atmod1i1 35143 |
. . . . . . . . . . 11
|
85 | 3, 6, 66, 68, 83, 84 | syl131anc 1339 |
. . . . . . . . . 10
|
86 | 8, 9 | hlatjass 34656 |
. . . . . . . . . . . 12
|
87 | 3, 6, 19, 45, 86 | syl13anc 1328 |
. . . . . . . . . . 11
|
88 | 8, 9 | hlatjcom 34654 |
. . . . . . . . . . . . 13
|
89 | 3, 6, 19, 88 | syl3anc 1326 |
. . . . . . . . . . . 12
|
90 | 89 | oveq1d 6665 |
. . . . . . . . . . 11
|
91 | 87, 90 | eqtr3d 2658 |
. . . . . . . . . 10
|
92 | 79, 85, 91 | 3brtr3d 4684 |
. . . . . . . . 9
|
93 | 1, 2, 8 | latlej2 17061 |
. . . . . . . . . 10
|
94 | 5, 51, 81, 93 | syl3anc 1326 |
. . . . . . . . 9
|
95 | 1, 8 | latjcl 17051 |
. . . . . . . . . . . 12
|
96 | 5, 32, 66, 95 | syl3anc 1326 |
. . . . . . . . . . 11
|
97 | 1, 16 | latmcl 17052 |
. . . . . . . . . . 11
|
98 | 5, 96, 68, 97 | syl3anc 1326 |
. . . . . . . . . 10
|
99 | 1, 8 | latjcl 17051 |
. . . . . . . . . . 11
|
100 | 5, 44, 51, 99 | syl3anc 1326 |
. . . . . . . . . 10
|
101 | 1, 2, 16 | latmlem12 17083 |
. . . . . . . . . 10
|
102 | 5, 98, 100, 81, 47, 101 | syl122anc 1335 |
. . . . . . . . 9
|
103 | 92, 94, 102 | mp2and 715 |
. . . . . . . 8
|
104 | | hlol 34648 |
. . . . . . . . . . 11
|
105 | 3, 104 | syl 17 |
. . . . . . . . . 10
|
106 | 1, 16 | latmassOLD 34516 |
. . . . . . . . . 10
|
107 | 105, 96, 68, 81, 106 | syl13anc 1328 |
. . . . . . . . 9
|
108 | 8, 9 | hlatjass 34656 |
. . . . . . . . . . . 12
|
109 | 3, 6, 7, 13, 108 | syl13anc 1328 |
. . . . . . . . . . 11
|
110 | 109 | eqcomd 2628 |
. . . . . . . . . 10
|
111 | 1, 2, 8 | latlej2 17061 |
. . . . . . . . . . . 12
|
112 | 5, 32, 81, 111 | syl3anc 1326 |
. . . . . . . . . . 11
|
113 | 1, 2, 16 | latleeqm2 17080 |
. . . . . . . . . . . 12
|
114 | 5, 81, 68, 113 | syl3anc 1326 |
. . . . . . . . . . 11
|
115 | 112, 114 | mpbid 222 |
. . . . . . . . . 10
|
116 | 110, 115 | oveq12d 6668 |
. . . . . . . . 9
|
117 | 107, 116 | eqtr2d 2657 |
. . . . . . . 8
|
118 | 1, 2, 8 | latlej1 17060 |
. . . . . . . . . 10
|
119 | 5, 51, 81, 118 | syl3anc 1326 |
. . . . . . . . 9
|
120 | 1, 2, 8, 16, 9 | atmod4i1 35152 |
. . . . . . . . 9
|
121 | 3, 45, 44, 47, 119, 120 | syl131anc 1339 |
. . . . . . . 8
|
122 | 103, 117,
121 | 3brtr4d 4685 |
. . . . . . 7
|
123 | 1, 16 | latmcl 17052 |
. . . . . . . . 9
|
124 | 5, 40, 81, 123 | syl3anc 1326 |
. . . . . . . 8
|
125 | 1, 2, 8 | latjlej1 17065 |
. . . . . . . 8
|
126 | 5, 124, 53, 38, 125 | syl13anc 1328 |
. . . . . . 7
|
127 | 122, 126 | mpd 15 |
. . . . . 6
|
128 | 64, 127 | eqbrtrrd 4677 |
. . . . 5
|
129 | 1, 2, 5, 18, 42, 55, 60, 128 | lattrd 17058 |
. . . 4
|
130 | 1, 8 | latj31 17099 |
. . . . 5
|
131 | 5, 49, 51, 38, 130 | syl13anc 1328 |
. . . 4
|
132 | 129, 131 | breqtrd 4679 |
. . 3
|
133 | 1, 8, 9 | hlatjcl 34653 |
. . . . . 6
|
134 | 3, 13, 45, 133 | syl3anc 1326 |
. . . . 5
|
135 | 1, 8 | latjcl 17051 |
. . . . 5
|
136 | 5, 134, 49, 135 | syl3anc 1326 |
. . . 4
|
137 | 1, 2, 16 | latlem12 17078 |
. . . 4
|
138 | 5, 18, 21, 136, 137 | syl13anc 1328 |
. . 3
|
139 | 36, 132, 138 | mpbi2and 956 |
. 2
|
140 | 1, 2, 16 | latmle1 17076 |
. . . . 5
|
141 | 5, 44, 47, 140 | syl3anc 1326 |
. . . 4
|
142 | 1, 2, 8 | latlej2 17061 |
. . . . . 6
|
143 | 5, 26, 28, 142 | syl3anc 1326 |
. . . . 5
|
144 | 1, 2, 8 | latjle12 17062 |
. . . . . 6
|
145 | 5, 28, 32, 21, 144 | syl13anc 1328 |
. . . . 5
|
146 | 143, 24, 145 | mpbi2and 956 |
. . . 4
|
147 | 1, 2, 5, 49, 44, 21, 141, 146 | lattrd 17058 |
. . 3
|
148 | 1, 2, 8, 16, 9 | llnmod2i2 35149 |
. . 3
|
149 | 3, 21, 49, 13, 45, 147, 148 | syl321anc 1348 |
. 2
|
150 | 139, 149 | breqtrrd 4681 |
1
|