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Theorem relsset 29101
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 29068 . . 3  |-  SSet  =  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  ) ) )
2 difss 3624 . . 3  |-  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  )
) )  C_  ( _V  X.  _V )
31, 2eqsstri 3527 . 2  |-  SSet  C_  ( _V  X.  _V )
4 df-rel 4999 . 2  |-  ( Rel 
SSet 
<-> 
SSet  C_  ( _V  X.  _V ) )
53, 4mpbir 209 1  |-  Rel  SSet
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3106    \ cdif 3466    C_ wss 3469    _E cep 4782    X. cxp 4990   ran crn 4993   Rel wrel 4997    (x) ctxp 29042   SSetcsset 29044
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-v 3108  df-dif 3472  df-in 3476  df-ss 3483  df-rel 4999  df-sset 29068
This theorem is referenced by:  brsset  29102  idsset  29103
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