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Theorem nfopab 3816
Description: Bound-variable hypothesis builder for class abstraction. (Contributed by NM, 1-Sep-1999.) (Unnecessary distinct variable restrictions were removed by Andrew Salmon, 11-Jul-2011.)
Hypothesis
Ref Expression
nfopab.1  F/
Assertion
Ref Expression
nfopab  F/_ { <. , 
>.  |  }
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem nfopab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-opab 3810 . 2  { <. ,  >.  |  }  {  |  <. ,  >.  }
2 nfv 1418 . . . . . 6  F/  <. ,  >.
3 nfopab.1 . . . . . 6  F/
42, 3nfan 1454 . . . . 5  F/  <. ,  >.
54nfex 1525 . . . 4  F/ 
<. ,  >.
65nfex 1525 . . 3  F/  <. ,  >.
76nfab 2179 . 2  F/_ {  |  <. , 
>.  }
81, 7nfcxfr 2172 1  F/_ { <. , 
>.  |  }
Colors of variables: wff set class
Syntax hints:   wa 97   wceq 1242   F/wnf 1346  wex 1378   {cab 2023   F/_wnfc 2162   <.cop 3370   {copab 3808
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-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-opab 3810
This theorem is referenced by:  csbopabg  3826  nfmpt  3840  nfxp  4314  nfco  4444  nfcnv  4457
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