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Theorem ralab2 2699
Description: Universal quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab2.1
Assertion
Ref Expression
ralab2  {  |  }
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ralab2
StepHypRef Expression
1 df-ral 2305 . 2  {  |  }  {  |  }
2 nfsab1 2027 . . . 4  F/  {  |  }
3 nfv 1418 . . . 4  F/
42, 3nfim 1461 . . 3  F/  {  |  }
5 nfv 1418 . . 3  F/
6 eleq1 2097 . . . . 5  {  |  } 
{  |  }
7 abid 2025 . . . . 5  {  |  }
86, 7syl6bb 185 . . . 4  {  |  }
9 ralab2.1 . . . 4
108, 9imbi12d 223 . . 3  {  |  }
114, 5, 10cbval 1634 . 2  {  |  }
121, 11bitri 173 1  {  |  }
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   wcel 1390   {cab 2023  wral 2300
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-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-ral 2305
This theorem is referenced by:  ralrab2  2700  ssintab  3623
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