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Theorem rabn0m 3218
Description: Inhabited restricted class abstraction. (Contributed by Jim Kingdon, 18-Sep-2018.)
Assertion
Ref Expression
rabn0m  {  |  }
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rabn0m
StepHypRef Expression
1 df-rex 2286 . 2
2 rabid 2459 . . 3  {  |  }
32exbii 1474 . 2  {  |  }
4 nfv 1398 . . 3  F/  {  |  }
5 df-rab 2289 . . . . 5  {  |  }  {  |  }
65eleq2i 2082 . . . 4  {  |  }  {  |  }
7 nfsab1 2008 . . . 4  F/  {  |  }
86, 7nfxfr 1339 . . 3  F/  {  |  }
9 eleq1 2078 . . 3  {  |  }  {  |  }
104, 8, 9cbvex 1617 . 2  {  |  }  {  |  }
111, 3, 103bitr2ri 198 1  {  |  }
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wex 1358   wcel 1370   {cab 2004  wrex 2281   {crab 2284
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-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-11 1374  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-rex 2286  df-rab 2289
This theorem is referenced by:  exss  3933
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