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Theorem rabn0m 3239
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 2306 . 2
2 rabid 2479 . . 3  {  |  }
32exbii 1493 . 2  {  |  }
4 nfv 1418 . . 3  F/  {  |  }
5 df-rab 2309 . . . . 5  {  |  }  {  |  }
65eleq2i 2101 . . . 4  {  |  }  {  |  }
7 nfsab1 2027 . . . 4  F/  {  |  }
86, 7nfxfr 1360 . . 3  F/  {  |  }
9 eleq1 2097 . . 3  {  |  }  {  |  }
104, 8, 9cbvex 1636 . 2  {  |  }  {  |  }
111, 3, 103bitr2ri 198 1  {  |  }
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wex 1378   wcel 1390   {cab 2023  wrex 2301   {crab 2304
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-rex 2306  df-rab 2309
This theorem is referenced by:  exss  3954
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