ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rabeqbidva Structured version   Unicode version

Theorem rabeqbidva 2547
Description: Equality of restricted class abstractions. (Contributed by Mario Carneiro, 26-Jan-2017.)
Hypotheses
Ref Expression
rabeqbidva.1
rabeqbidva.2
Assertion
Ref Expression
rabeqbidva  {  |  }  {  |  }
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rabeqbidva
StepHypRef Expression
1 rabeqbidva.2 . . 3
21rabbidva 2542 . 2  {  |  }  {  |  }
3 rabeqbidva.1 . . 3
4 rabeq 2545 . . 3  {  |  }  {  |  }
53, 4syl 14 . 2  {  |  }  {  |  }
62, 5eqtrd 2069 1  {  |  }  {  |  }
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   wcel 1390   {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-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-bnd 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-ral 2305  df-rab 2309
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator