Proof of Theorem cdleme22eALTN
Step | Hyp | Ref
| Expression |
1 | | cdleme22eALT.n |
. . 3
  
        |
2 | | simp11 1037 |
. . . . 5
  
    
 


            
  |
3 | | hllat 32923 |
. . . . 5
   |
4 | 2, 3 | syl 17 |
. . . 4
  
    
 


            
  |
5 | | simp21l 1124 |
. . . . 5
  
    
 


            
  |
6 | | simp22l 1126 |
. . . . 5
  
    
 


            
  |
7 | | eqid 2450 |
. . . . . 6
         |
8 | | cdleme22.j |
. . . . . 6
     |
9 | | cdleme22.a |
. . . . . 6
     |
10 | 7, 8, 9 | hlatjcl 32926 |
. . . . 5
 
         |
11 | 2, 5, 6, 10 | syl3anc 1267 |
. . . 4
  
    
 


            
        |
12 | | simp12 1038 |
. . . . . 6
  
    
 


            
  |
13 | | simp3ll 1078 |
. . . . . . 7
  

             |
14 | 13 | 3ad2ant3 1030 |
. . . . . 6
  
    
 


            
  |
15 | | cdleme22.l |
. . . . . . 7
     |
16 | | cdleme22.m |
. . . . . . 7
     |
17 | | cdleme22.h |
. . . . . . 7
     |
18 | | cdleme22eALT.u |
. . . . . . 7
  
  |
19 | | cdleme22eALT.f |
. . . . . . 7
  
        |
20 | 15, 8, 16, 9, 17, 18, 19, 7 | cdleme1b 33786 |
. . . . . 6
      
      |
21 | 2, 12, 5, 6, 14, 20 | syl23anc 1274 |
. . . . 5
  
    
 


            
      |
22 | | simp31 1043 |
. . . . . . 7
  
    
 


            
  |
23 | 7, 8, 9 | hlatjcl 32926 |
. . . . . . 7
 
         |
24 | 2, 22, 14, 23 | syl3anc 1267 |
. . . . . 6
  
    
 


            
        |
25 | 7, 17 | lhpbase 33557 |
. . . . . . 7
       |
26 | 12, 25 | syl 17 |
. . . . . 6
  
    
 


            
      |
27 | 7, 16 | latmcl 16291 |
. . . . . 6
  
    
    
          |
28 | 4, 24, 26, 27 | syl3anc 1267 |
. . . . 5
  
    
 


            
          |
29 | 7, 8 | latjcl 16290 |
. . . . 5
 
      
                  |
30 | 4, 21, 28, 29 | syl3anc 1267 |
. . . 4
  
    
 


            
            |
31 | 7, 15, 16 | latmle1 16315 |
. . . 4
  
    
          
   
     
    |
32 | 4, 11, 30, 31 | syl3anc 1267 |
. . 3
  
    
 


            
   
     
    |
33 | 1, 32 | syl5eqbr 4435 |
. 2
  
    
 


            
    |
34 | | simp21 1040 |
. . . . 5
  
    
 


            

   |
35 | | simp13 1039 |
. . . . 5
  
    
 


            
  |
36 | | simp321 1157 |
. . . . . 6
  
    
 


            
  |
37 | | simp322 1158 |
. . . . . 6
  
    
 


            
  |
38 | 36, 37 | jca 535 |
. . . . 5
  
    
 


            

   |
39 | | simp23 1042 |
. . . . 5
  
    
 


            
  |
40 | | simp323 1159 |
. . . . 5
  
    
 


            
      |
41 | 15, 8, 16, 9, 17, 18 | cdleme22a 33901 |
. . . . 5
      
   
        |
42 | 2, 12, 34, 6, 35, 38, 39, 40, 41 | syl233anc 1296 |
. . . 4
  
    
 


            
  |
43 | 42 | oveq2d 6304 |
. . 3
  
    
 


            
      |
44 | | cdleme22eALT.o |
. . . . 5
  
        |
45 | 44 | oveq1i 6298 |
. . . 4
      
        |
46 | | simp21r 1125 |
. . . . . 6
  
    
 


            
  |
47 | 15, 8, 16, 9, 17, 18 | cdleme0a 33771 |
. . . . . 6
      
    |
48 | 2, 12, 5, 46, 6, 39, 47 | syl222anc 1283 |
. . . . 5
  
    
 


            
  |
49 | | simp3rl 1080 |
. . . . . . . 8
  

             |
50 | 49 | 3ad2ant3 1030 |
. . . . . . 7
  
    
 


            
  |
51 | | cdleme22eALT.g |
. . . . . . . 8
  
        |
52 | 15, 8, 16, 9, 17, 18, 51, 7 | cdleme1b 33786 |
. . . . . . 7
      
      |
53 | 2, 12, 5, 6, 50, 52 | syl23anc 1274 |
. . . . . 6
  
    
 


            
      |
54 | 7, 8, 9 | hlatjcl 32926 |
. . . . . . . 8
 
         |
55 | 2, 35, 50, 54 | syl3anc 1267 |
. . . . . . 7
  
    
 


            
        |
56 | 7, 16 | latmcl 16291 |
. . . . . . 7
  
    
    
          |
57 | 4, 55, 26, 56 | syl3anc 1267 |
. . . . . 6
  
    
 


            
          |
58 | 7, 8 | latjcl 16290 |
. . . . . 6
 
      
                  |
59 | 4, 53, 57, 58 | syl3anc 1267 |
. . . . 5
  
    
 


            
            |
60 | 15, 8, 16, 9, 17, 18 | cdlemeulpq 33780 |
. . . . . 6
           |
61 | 2, 12, 5, 6, 60 | syl22anc 1268 |
. . . . 5
  
    
 


            
    |
62 | 7, 15, 8, 16, 9 | atmod2i1 33420 |
. . . . 5
  
                
  
   
                      |
63 | 2, 48, 11, 59, 61, 62 | syl131anc 1280 |
. . . 4
  
    
 


            
   
                      |
64 | 45, 63 | syl5req 2497 |
. . 3
  
    
 


            
                |
65 | 42 | oveq2d 6304 |
. . . . . 6
  
    
 


            
      |
66 | 40, 65 | eqtr3d 2486 |
. . . . 5
  
    
 


            
      |
67 | 7, 8, 9 | hlatjcl 32926 |
. . . . . . . 8
 
         |
68 | 2, 35, 48, 67 | syl3anc 1267 |
. . . . . . 7
  
    
 


            
        |
69 | 7, 9 | atbase 32849 |
. . . . . . . 8
       |
70 | 50, 69 | syl 17 |
. . . . . . 7
  
    
 


            
      |
71 | 7, 15, 8 | latlej1 16299 |
. . . . . . 7
  
    
    
        |
72 | 4, 68, 70, 71 | syl3anc 1267 |
. . . . . 6
  
    
 


            
        |
73 | 8, 9 | hlatj32 32931 |
. . . . . . . 8
  
    
       |
74 | 2, 35, 48, 50, 73 | syl13anc 1269 |
. . . . . . 7
  
    
 


            
      
   |
75 | 7, 9 | atbase 32849 |
. . . . . . . . . 10
       |
76 | 48, 75 | syl 17 |
. . . . . . . . 9
  
    
 


            
      |
77 | 7, 8 | latj32 16336 |
. . . . . . . . 9
      
                          
 
   |
78 | 4, 70, 76, 57, 77 | syl13anc 1269 |
. . . . . . . 8
  
    
 


            
 
          
 
   |
79 | 7, 8 | latj32 16336 |
. . . . . . . . . 10
  
                                    |
80 | 4, 53, 57, 76, 79 | syl13anc 1269 |
. . . . . . . . 9
  
    
 


            
                  |
81 | 7, 8, 9 | hlatjcl 32926 |
. . . . . . . . . . . . . . . . . . 19
 
         |
82 | 2, 5, 50, 81 | syl3anc 1267 |
. . . . . . . . . . . . . . . . . 18
  
    
 


            
        |
83 | 15, 8, 9 | hlatlej1 32934 |
. . . . . . . . . . . . . . . . . . 19
 

    |
84 | 2, 5, 50, 83 | syl3anc 1267 |
. . . . . . . . . . . . . . . . . 18
  
    
 


            
    |
85 | 7, 15, 8, 16, 9 | atmod3i1 33423 |
. . . . . . . . . . . . . . . . . 18
  
                      
     |
86 | 2, 5, 82, 26, 84, 85 | syl131anc 1280 |
. . . . . . . . . . . . . . . . 17
  
    
 


            
        
     |
87 | | eqid 2450 |
. . . . . . . . . . . . . . . . . . . 20
         |
88 | 15, 8, 87, 9, 17 | lhpjat2 33580 |
. . . . . . . . . . . . . . . . . . 19
               |
89 | 2, 12, 34, 88 | syl21anc 1266 |
. . . . . . . . . . . . . . . . . 18
  
    
 


            
        |
90 | 89 | oveq2d 6304 |
. . . . . . . . . . . . . . . . 17
  
    
 


            
   
            |
91 | | hlol 32921 |
. . . . . . . . . . . . . . . . . . 19
   |
92 | 2, 91 | syl 17 |
. . . . . . . . . . . . . . . . . 18
  
    
 


            
  |
93 | 7, 16, 87 | olm11 32787 |
. . . . . . . . . . . . . . . . . 18
  
        
         |
94 | 92, 82, 93 | syl2anc 666 |
. . . . . . . . . . . . . . . . 17
  
    
 


            
            |
95 | 86, 90, 94 | 3eqtrd 2488 |
. . . . . . . . . . . . . . . 16
  
    
 


            
          |
96 | 95 | oveq1d 6303 |
. . . . . . . . . . . . . . 15
  
    
 


            
              |
97 | 18 | oveq2i 6299 |
. . . . . . . . . . . . . . . . . . 19
     
   |
98 | 15, 8, 9 | hlatlej2 32935 |
. . . . . . . . . . . . . . . . . . . . 21
 

    |
99 | 2, 5, 6, 98 | syl3anc 1267 |
. . . . . . . . . . . . . . . . . . . 20
  
    
 


            
    |
100 | 7, 15, 8, 16, 9 | atmod3i1 33423 |
. . . . . . . . . . . . . . . . . . . 20
  
                      
     |
101 | 2, 6, 11, 26, 99, 100 | syl131anc 1280 |
. . . . . . . . . . . . . . . . . . 19
  
    
 


            
   
          |
102 | 97, 101 | syl5eq 2496 |
. . . . . . . . . . . . . . . . . 18
  
    
 


            
    
     |
103 | | simp22 1041 |
. . . . . . . . . . . . . . . . . . . 20
  
    
 


            

   |
104 | 15, 8, 87, 9, 17 | lhpjat2 33580 |
. . . . . . . . . . . . . . . . . . . 20
               |
105 | 2, 12, 103, 104 | syl21anc 1266 |
. . . . . . . . . . . . . . . . . . 19
  
    
 


            
        |
106 | 105 | oveq2d 6304 |
. . . . . . . . . . . . . . . . . 18
  
    
 


            
   
            |
107 | 7, 16, 87 | olm11 32787 |
. . . . . . . . . . . . . . . . . . 19
  
        
         |
108 | 92, 11, 107 | syl2anc 666 |
. . . . . . . . . . . . . . . . . 18
  
    
 


            
            |
109 | 102, 106,
108 | 3eqtrd 2488 |
. . . . . . . . . . . . . . . . 17
  
    
 


            
      |
110 | 109 | oveq1d 6303 |
. . . . . . . . . . . . . . . 16
  
    
 


            
          
       |
111 | 7, 9 | atbase 32849 |
. . . . . . . . . . . . . . . . . 18
       |
112 | 5, 111 | syl 17 |
. . . . . . . . . . . . . . . . 17
  
    
 


            
      |
113 | 7, 16 | latmcl 16291 |
. . . . . . . . . . . . . . . . . 18
  
    
    
          |
114 | 4, 82, 26, 113 | syl3anc 1267 |
. . . . . . . . . . . . . . . . 17
  
    
 


            
          |
115 | 7, 9 | atbase 32849 |
. . . . . . . . . . . . . . . . . 18
       |
116 | 6, 115 | syl 17 |
. . . . . . . . . . . . . . . . 17
  
    
 


            
      |
117 | 7, 8 | latj32 16336 |
. . . . . . . . . . . . . . . . 17
  
                                    |
118 | 4, 112, 114, 116, 117 | syl13anc 1269 |
. . . . . . . . . . . . . . . 16
  
    
 


            
                  |
119 | 110, 118 | eqtr4d 2487 |
. . . . . . . . . . . . . . 15
  
    
 


            
            
 
   |
120 | 8, 9 | hlatj32 32931 |
. . . . . . . . . . . . . . . 16
  
    
       |
121 | 2, 5, 6, 50, 120 | syl13anc 1269 |
. . . . . . . . . . . . . . 15
  
    
 


            
      
   |
122 | 96, 119, 121 | 3eqtr4rd 2495 |
. . . . . . . . . . . . . 14
  
    
 


            
      
       |
123 | 7, 8 | latj32 16336 |
. . . . . . . . . . . . . . 15
  
   
      
                         |
124 | 4, 116, 76, 114, 123 | syl13anc 1269 |
. . . . . . . . . . . . . 14
  
    
 


            
            
 
   |
125 | 122, 124 | eqtrd 2484 |
. . . . . . . . . . . . 13
  
    
 


            
        
 
   |
126 | 125 | oveq2d 6304 |
. . . . . . . . . . . 12
  
    
 


            
 
                    |
127 | 7, 8 | latjcl 16290 |
. . . . . . . . . . . . . 14
  
    
    
          |
128 | 4, 11, 70, 127 | syl3anc 1267 |
. . . . . . . . . . . . 13
  
    
 


            
          |
129 | 7, 15, 8 | latlej2 16300 |
. . . . . . . . . . . . . 14
  
    
    
  
   |
130 | 4, 11, 70, 129 | syl3anc 1267 |
. . . . . . . . . . . . 13
  
    
 


            
  
   |
131 | 7, 15, 8, 16, 9 | atmod1i1 33416 |
. . . . . . . . . . . . 13
  
                 
    
     
       |
132 | 2, 50, 76, 128, 130, 131 | syl131anc 1280 |
. . . . . . . . . . . 12
  
    
 


            
    
     
       |
133 | 51 | oveq1i 6298 |
. . . . . . . . . . . . 13
      
        |
134 | 7, 8, 9 | hlatjcl 32926 |
. . . . . . . . . . . . . . 15
 
         |
135 | 2, 50, 48, 134 | syl3anc 1267 |
. . . . . . . . . . . . . 14
  
    
 


            
        |
136 | 7, 8 | latjcl 16290 |
. . . . . . . . . . . . . . 15
 
      
                  |
137 | 4, 116, 114, 136 | syl3anc 1267 |
. . . . . . . . . . . . . 14
  
    
 


            
            |
138 | 15, 8, 9 | hlatlej2 32935 |
. . . . . . . . . . . . . . 15
 

    |
139 | 2, 50, 48, 138 | syl3anc 1267 |
. . . . . . . . . . . . . 14
  
    
 


            
    |
140 | 7, 15, 8, 16, 9 | atmod2i1 33420 |
. . . . . . . . . . . . . 14
  
                
  
   
                      |
141 | 2, 48, 135, 137, 139, 140 | syl131anc 1280 |
. . . . . . . . . . . . 13
  
    
 


            
   
                      |
142 | 133, 141 | syl5eq 2496 |
. . . . . . . . . . . 12
  
    
 


            
    
           |
143 | 126, 132,
142 | 3eqtr4rd 2495 |
. . . . . . . . . . 11
  
    
 


            
            |
144 | 7, 15, 8 | latlej1 16299 |
. . . . . . . . . . . . . . 15
  
    
    
        |
145 | 4, 11, 70, 144 | syl3anc 1267 |
. . . . . . . . . . . . . 14
  
    
 


            
        |
146 | 7, 15, 4, 76, 11, 128, 61, 145 | lattrd 16297 |
. . . . . . . . . . . . 13
  
    
 


            
  
   |
147 | 7, 15, 16 | latleeqm1 16318 |
. . . . . . . . . . . . . 14
 
      
          
         |
148 | 4, 76, 128, 147 | syl3anc 1267 |
. . . . . . . . . . . . 13
  
    
 


            
        
     |
149 | 146, 148 | mpbid 214 |
. . . . . . . . . . . 12
  
    
 


            
        |
150 | 149 | oveq2d 6304 |
. . . . . . . . . . 11
  
    
 


            
    
       |
151 | 143, 150 | eqtrd 2484 |
. . . . . . . . . 10
  
    
 


            
      |
152 | 151 | oveq1d 6303 |
. . . . . . . . 9
  
    
 


            
          
       |
153 | 80, 152 | eqtrd 2484 |
. . . . . . . 8
  
    
 


            
                  |
154 | 15, 8, 9 | hlatlej2 32935 |
. . . . . . . . . . . 12
 

    |
155 | 2, 35, 50, 154 | syl3anc 1267 |
. . . . . . . . . . 11
  
    
 


            
    |
156 | 7, 15, 8, 16, 9 | atmod3i1 33423 |
. . . . . . . . . . 11
                 
       
     |
157 | 2, 50, 55, 26, 155, 156 | syl131anc 1280 |
. . . . . . . . . 10
  
    
 


            
        
     |
158 | | simp33r 1135 |
. . . . . . . . . . . 12
  
    
 


            

   |
159 | 15, 8, 87, 9, 17 | lhpjat2 33580 |
. . . . . . . . . . . 12
               |
160 | 2, 12, 158, 159 | syl21anc 1266 |
. . . . . . . . . . 11
  
    
 


            
        |
161 | 160 | oveq2d 6304 |
. . . . . . . . . 10
  
    
 


            
        
       |
162 | 7, 16, 87 | olm11 32787 |
. . . . . . . . . . 11
  
        
         |
163 | 92, 55, 162 | syl2anc 666 |
. . . . . . . . . 10
  
    
 


            
            |
164 | 157, 161,
163 | 3eqtrrd 2489 |
. . . . . . . . 9
  
    
 


            
          |
165 | 164 | oveq1d 6303 |
. . . . . . . 8
  
    
 


            
              |
166 | 78, 153, 165 | 3eqtr4rd 2495 |
. . . . . . 7
  
    
 


            
              |
167 | 74, 166 | eqtrd 2484 |
. . . . . 6
  
    
 


            
        
 
   |
168 | 72, 167 | breqtrd 4426 |
. . . . 5
  
    
 


            
            |
169 | 66, 168 | eqbrtrd 4422 |
. . . 4
  
    
 


            
            |
170 | 7, 8 | latjcl 16290 |
. . . . . 6
  
        
    
              |
171 | 4, 59, 76, 170 | syl3anc 1267 |
. . . . 5
  
    
 


            
              |
172 | 7, 15, 16 | latleeqm1 16318 |
. . . . 5
  
    
               
                         |
173 | 4, 11, 171, 172 | syl3anc 1267 |
. . . 4
  
    
 


            
                            |
174 | 169, 173 | mpbid 214 |
. . 3
  
    
 


            
                |
175 | 43, 64, 174 | 3eqtr2rd 2491 |
. 2
  
    
 


            
      |
176 | 33, 175 | breqtrd 4426 |
1
  
    
 


            
    |