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

Theorem relsset 25725
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 25692 . . 3  |-  SSet  =  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  ) ) )
2 difss 3466 . . 3  |-  ( ( _V  X.  _V )  \  ran  (  _E  (x)  ( _V  \  _E  )
) )  C_  ( _V  X.  _V )
31, 2eqsstri 3370 . 2  |-  SSet  C_  ( _V  X.  _V )
4 df-rel 4877 . 2  |-  ( Rel 
SSet 
<-> 
SSet  C_  ( _V  X.  _V ) )
53, 4mpbir 201 1  |-  Rel  SSet
Colors of variables: wff set class
Syntax hints:   _Vcvv 2948    \ cdif 3309    C_ wss 3312    _E cep 4484    X. cxp 4868   ran crn 4871   Rel wrel 4875    (x) ctxp 25666   SSetcsset 25668
This theorem is referenced by:  brsset  25726  idsset  25727
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-rel 4877  df-sset 25692
  Copyright terms: Public domain W3C validator