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Theorem relsset 25453
Description: The subset class is a relationship. (Contributed by Scott Fenton, 31-Mar-2012.)
Assertion
Ref Expression
relsset  |-  Rel  SSet

Proof of Theorem relsset
StepHypRef Expression
1 df-sset 25422 . . 3  |-  SSet  =  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  ) ) )
2 difss 3418 . . 3  |-  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  )
) )  C_  ( _V  X.  _V )
31, 2eqsstri 3322 . 2  |-  SSet  C_  ( _V  X.  _V )
4 df-rel 4826 . 2  |-  ( Rel 
SSet 
<-> 
SSet  C_  ( _V  X.  _V ) )
53, 4mpbir 201 1  |-  Rel  SSet
Colors of variables: wff set class
Syntax hints:   _Vcvv 2900    \ cdif 3261    C_ wss 3264    _E cep 4434    X. cxp 4817   ran crn 4820   Rel wrel 4824    (x) ctxp 25398   SSetcsset 25400
This theorem is referenced by:  brsset  25454  idsset  25455
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-v 2902  df-dif 3267  df-in 3271  df-ss 3278  df-rel 4826  df-sset 25422
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