Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  relsset Unicode version

Theorem relsset 24499
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 24468 . . 3  |-  SSet  =  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  ) ) )
2 difss 3316 . . 3  |-  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  )
) )  C_  ( _V  X.  _V )
31, 2eqsstri 3221 . 2  |-  SSet  C_  ( _V  X.  _V )
4 df-rel 4712 . 2  |-  ( Rel 
SSet 
<-> 
SSet  C_  ( _V  X.  _V ) )
53, 4mpbir 200 1  |-  Rel  SSet
Colors of variables: wff set class
Syntax hints:   _Vcvv 2801    \ cdif 3162    C_ wss 3165    _E cep 4319    X. cxp 4703   ran crn 4706   Rel wrel 4710    (x) ctxp 24444   SSetcsset 24446
This theorem is referenced by:  brsset  24500  idsset  24501
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-rel 4712  df-sset 24468
  Copyright terms: Public domain W3C validator