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Theorem cbvrabcsf 2905
Description: A more general version of cbvrab 2549 with no distinct variable restrictions. (Contributed by Andrew Salmon, 13-Jul-2011.)
Hypotheses
Ref Expression
cbvralcsf.1  F/_
cbvralcsf.2  F/_
cbvralcsf.3  F/
cbvralcsf.4  F/
cbvralcsf.5
cbvralcsf.6
Assertion
Ref Expression
cbvrabcsf  {  |  }  {  |  }

Proof of Theorem cbvrabcsf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nfv 1418 . . . 4  F/
2 nfcsb1v 2876 . . . . . 6  F/_ [_  ]_
32nfcri 2169 . . . . 5  F/  [_  ]_
4 nfs1v 1812 . . . . 5  F/
53, 4nfan 1454 . . . 4  F/  [_  ]_
6 id 19 . . . . . 6
7 csbeq1a 2854 . . . . . 6  [_  ]_
86, 7eleq12d 2105 . . . . 5 
[_  ]_
9 sbequ12 1651 . . . . 5
108, 9anbi12d 442 . . . 4  [_  ]_
111, 5, 10cbvab 2157 . . 3  {  |  }  {  |  [_  ]_  }
12 nfcv 2175 . . . . . . 7  F/_
13 cbvralcsf.1 . . . . . . 7  F/_
1412, 13nfcsb 2878 . . . . . 6  F/_ [_  ]_
1514nfcri 2169 . . . . 5  F/  [_  ]_
16 cbvralcsf.3 . . . . . 6  F/
1716nfsb 1819 . . . . 5  F/
1815, 17nfan 1454 . . . 4  F/  [_  ]_
19 nfv 1418 . . . 4  F/
20 id 19 . . . . . 6
21 csbeq1 2849 . . . . . . 7  [_  ]_  [_  ]_
22 df-csb 2847 . . . . . . . 8  [_  ]_  {  |  [.  ].  }
23 cbvralcsf.2 . . . . . . . . . . . 12  F/_
2423nfcri 2169 . . . . . . . . . . 11  F/
25 cbvralcsf.5 . . . . . . . . . . . 12
2625eleq2d 2104 . . . . . . . . . . 11
2724, 26sbie 1671 . . . . . . . . . 10
28 sbsbc 2762 . . . . . . . . . 10  [.  ].
2927, 28bitr3i 175 . . . . . . . . 9  [.  ].
3029abbi2i 2149 . . . . . . . 8  {  |  [.  ].  }
3122, 30eqtr4i 2060 . . . . . . 7  [_  ]_
3221, 31syl6eq 2085 . . . . . 6  [_  ]_
3320, 32eleq12d 2105 . . . . 5  [_  ]_
34 sbequ 1718 . . . . . 6
35 cbvralcsf.4 . . . . . . 7  F/
36 cbvralcsf.6 . . . . . . 7
3735, 36sbie 1671 . . . . . 6
3834, 37syl6bb 185 . . . . 5
3933, 38anbi12d 442 . . . 4  [_  ]_
4018, 19, 39cbvab 2157 . . 3  {  | 
[_  ]_  }  {  |  }
4111, 40eqtri 2057 . 2  {  |  }  {  |  }
42 df-rab 2309 . 2  {  |  }  {  |  }
43 df-rab 2309 . 2  {  |  }  {  |  }
4441, 42, 433eqtr4i 2067 1  {  |  }  {  |  }
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   F/wnf 1346   wcel 1390  wsb 1642   {cab 2023   F/_wnfc 2162   {crab 2304   [.wsbc 2758   [_csb 2846
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309  df-sbc 2759  df-csb 2847
This theorem is referenced by: (None)
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