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

Theorem relsset 33374
Description: The subset class is a binary relation. (Contributed by Scott Fenton, 31-Mar-2012.)
Assertion
Ref Expression
relsset Rel SSet

Proof of Theorem relsset
StepHypRef Expression
1 df-sset 33342 . . 3 SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2 difss 4093 . . 3 ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
31, 2eqsstri 3986 . 2 SSet ⊆ (V × V)
4 df-rel 5549 . 2 (Rel SSet SSet ⊆ (V × V))
53, 4mpbir 234 1 Rel SSet
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3480  cdif 3916  wss 3919   E cep 5451   × cxp 5540  ran crn 5543  Rel wrel 5547  ctxp 33316   SSet csset 33318
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-12 2179  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-dif 3922  df-in 3926  df-ss 3936  df-rel 5549  df-sset 33342
This theorem is referenced by:  brsset  33375  idsset  33376
  Copyright terms: Public domain W3C validator