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Theorem relsset 30213
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 30180 . . 3  |-  SSet  =  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  ) ) )
2 difss 3569 . . 3  |-  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  )
) )  C_  ( _V  X.  _V )
31, 2eqsstri 3471 . 2  |-  SSet  C_  ( _V  X.  _V )
4 df-rel 4829 . 2  |-  ( Rel 
SSet 
<-> 
SSet  C_  ( _V  X.  _V ) )
53, 4mpbir 209 1  |-  Rel  SSet
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3058    \ cdif 3410    C_ wss 3413    _E cep 4731    X. cxp 4820   ran crn 4823   Rel wrel 4827    (x) ctxp 30154   SSetcsset 30156
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-v 3060  df-dif 3416  df-in 3420  df-ss 3427  df-rel 4829  df-sset 30180
This theorem is referenced by:  brsset  30214  idsset  30215
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