Step | Hyp | Ref
| Expression |
1 | | isleag.g |
. . . . 5

TarskiG |
2 | | elex 3054 |
. . . . 5
 TarskiG   |
3 | | fveq2 5865 |
. . . . . . . . . . . 12
           |
4 | | isleag.p |
. . . . . . . . . . . 12
     |
5 | 3, 4 | syl6eqr 2503 |
. . . . . . . . . . 11
       |
6 | 5 | oveq1d 6305 |
. . . . . . . . . 10
       ..^    ..^    |
7 | 6 | eleq2d 2514 |
. . . . . . . . 9
        ..^    ..^     |
8 | 6 | eleq2d 2514 |
. . . . . . . . 9
        ..^    ..^     |
9 | 7, 8 | anbi12d 717 |
. . . . . . . 8
       
 ..^ 
      ..^      ..^    ..^      |
10 | | fveq2 5865 |
. . . . . . . . . . 11
 inA  inA    |
11 | 10 | breqd 4413 |
. . . . . . . . . 10
   inA                    
 inA                        |
12 | | fveq2 5865 |
. . . . . . . . . . 11
 cgrA  cgrA    |
13 | 12 | breqd 4413 |
. . . . . . . . . 10
                     cgrA                                    cgrA                    |
14 | 11, 13 | anbi12d 717 |
. . . . . . . . 9
    inA                                        cgrA                    inA                                        cgrA                     |
15 | 5, 14 | rexeqbidv 3002 |
. . . . . . . 8
  
       inA                                        cgrA                     inA                                        cgrA                     |
16 | 9, 15 | anbi12d 717 |
. . . . . . 7
        
 ..^ 
      ..^           inA                                        cgrA                       ..^    ..^      inA                                        cgrA                      |
17 | 16 | opabbidv 4466 |
. . . . . 6
           
 ..^ 
      ..^           inA                                        cgrA                            ..^    ..^      inA                                        cgrA                      |
18 | | df-leag 24882 |
. . . . . 6
≤∠
           
 ..^ 
      ..^           inA                                        cgrA                      |
19 | | ovex 6318 |
. . . . . . . 8
  ..^   |
20 | | xpexg 6593 |
. . . . . . . 8
    ..^    ..^      ..^    ..^     |
21 | 19, 19, 20 | mp2an 678 |
. . . . . . 7
   ..^    ..^    |
22 | | opabssxp 4909 |
. . . . . . 7
        ..^ 
  ..^   
  inA                                        cgrA                       ..^    ..^    |
23 | 21, 22 | ssexi 4548 |
. . . . . 6
        ..^ 
  ..^   
  inA                                        cgrA                     |
24 | 17, 18, 23 | fvmpt 5948 |
. . . . 5
 ≤∠          ..^ 
  ..^   
  inA                                        cgrA                      |
25 | 1, 2, 24 | 3syl 18 |
. . . 4
 ≤∠     
    ..^    ..^   
  inA                                        cgrA                      |
26 | 25 | breqd 4413 |
. . 3
         ≤∠        
               ..^ 
  ..^   
  inA                                        cgrA                              |
27 | | simpr 463 |
. . . . . . . . . 10
                       |
28 | 27 | fveq1d 5867 |
. . . . . . . . 9
                               |
29 | 27 | fveq1d 5867 |
. . . . . . . . 9
                               |
30 | 27 | fveq1d 5867 |
. . . . . . . . 9
                               |
31 | 28, 29, 30 | s3eqd 12959 |
. . . . . . . 8
                                                                       |
32 | 31 | breq2d 4414 |
. . . . . . 7
                 inA                      inA                                          |
33 | | simpl 459 |
. . . . . . . . . 10
                       |
34 | 33 | fveq1d 5867 |
. . . . . . . . 9
                               |
35 | 33 | fveq1d 5867 |
. . . . . . . . 9
                               |
36 | 33 | fveq1d 5867 |
. . . . . . . . 9
                               |
37 | 34, 35, 36 | s3eqd 12959 |
. . . . . . . 8
                                                                       |
38 | | eqidd 2452 |
. . . . . . . . 9
                 |
39 | 28, 29, 38 | s3eqd 12959 |
. . . . . . . 8
                                                         |
40 | 37, 39 | breq12d 4415 |
. . . . . . 7
                                   cgrA                
                                     cgrA                                |
41 | 32, 40 | anbi12d 717 |
. . . . . 6
                  inA                                        cgrA                    inA                                                                            cgrA                                 |
42 | 41 | rexbidv 2901 |
. . . . 5
                   inA                                        cgrA                     inA                                                                            cgrA                                 |
43 | | eqid 2451 |
. . . . 5
        ..^ 
  ..^   
  inA                                        cgrA                            ..^    ..^      inA                                        cgrA                     |
44 | 42, 43 | brab2a 4884 |
. . . 4
                ..^ 
  ..^   
  inA                                        cgrA                          
          ..^          ..^      inA                                                                            cgrA                                 |
45 | 44 | a1i 11 |
. . 3
                 ..^ 
  ..^   
  inA                                        cgrA                          
          ..^          ..^      inA                                                                            cgrA                                  |
46 | | isleag.d |
. . . . . . . . 9
   |
47 | | s3fv0 12985 |
. . . . . . . . 9
             |
48 | 46, 47 | syl 17 |
. . . . . . . 8
             |
49 | | isleag.e |
. . . . . . . . 9
   |
50 | | s3fv1 12986 |
. . . . . . . . 9
             |
51 | 49, 50 | syl 17 |
. . . . . . . 8
             |
52 | | isleag.f |
. . . . . . . . 9
   |
53 | | s3fv2 12987 |
. . . . . . . . 9
             |
54 | 52, 53 | syl 17 |
. . . . . . . 8
             |
55 | 48, 51, 54 | s3eqd 12959 |
. . . . . . 7
                                             |
56 | 55 | breq2d 4414 |
. . . . . 6
   inA                                      
 inA            |
57 | | isleag.a |
. . . . . . . . 9
   |
58 | | s3fv0 12985 |
. . . . . . . . 9
             |
59 | 57, 58 | syl 17 |
. . . . . . . 8
             |
60 | | isleag.b |
. . . . . . . . 9
   |
61 | | s3fv1 12986 |
. . . . . . . . 9
             |
62 | 60, 61 | syl 17 |
. . . . . . . 8
             |
63 | | isleag.c |
. . . . . . . . 9
   |
64 | | s3fv2 12987 |
. . . . . . . . 9
             |
65 | 63, 64 | syl 17 |
. . . . . . . 8
             |
66 | 59, 62, 65 | s3eqd 12959 |
. . . . . . 7
                                             |
67 | | eqidd 2452 |
. . . . . . . 8
   |
68 | 48, 51, 67 | s3eqd 12959 |
. . . . . . 7
                                   |
69 | 66, 68 | breq12d 4415 |
. . . . . 6
                                       cgrA                                    cgrA            |
70 | 56, 69 | anbi12d 717 |
. . . . 5
    inA                                                                            cgrA                                inA                cgrA             |
71 | 70 | rexbidv 2901 |
. . . 4
     inA                                                                            cgrA                                 inA                cgrA             |
72 | 71 | anbi2d 710 |
. . 3
            ..^          ..^      inA                                                                            cgrA                              
          ..^          ..^      inA                cgrA              |
73 | 26, 45, 72 | 3bitrd 283 |
. 2
         ≤∠        
          ..^          ..^      inA                cgrA              |
74 | 57, 60, 63 | s3cld 12966 |
. . . . . 6
       Word   |
75 | | s3len 12988 |
. . . . . . 7
           |
76 | 75 | a1i 11 |
. . . . . 6
          
  |
77 | 74, 76 | jca 535 |
. . . . 5
        Word          
   |
78 | | fvex 5875 |
. . . . . . 7
     |
79 | 4, 78 | eqeltri 2525 |
. . . . . 6
 |
80 | | 3nn0 10887 |
. . . . . 6
 |
81 | | wrdmap 12698 |
. . . . . 6
 
         Word          
       
 ..^     |
82 | 79, 80, 81 | mp2an 678 |
. . . . 5
        Word          
       
 ..^    |
83 | 77, 82 | sylib 200 |
. . . 4
       
 ..^    |
84 | 46, 49, 52 | s3cld 12966 |
. . . . . 6
       Word   |
85 | | s3len 12988 |
. . . . . . 7
           |
86 | 85 | a1i 11 |
. . . . . 6
          
  |
87 | 84, 86 | jca 535 |
. . . . 5
        Word          
   |
88 | | wrdmap 12698 |
. . . . . 6
 
         Word          
       
 ..^     |
89 | 79, 80, 88 | mp2an 678 |
. . . . 5
        Word          
       
 ..^    |
90 | 87, 89 | sylib 200 |
. . . 4
       
 ..^    |
91 | 83, 90 | jca 535 |
. . 3
        
 ..^        
 ..^     |
92 | 91 | biantrurd 511 |
. 2
     inA                cgrA         
          ..^          ..^      inA                cgrA              |
93 | 73, 92 | bitr4d 260 |
1
         ≤∠        

  inA                cgrA             |