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Theorem relsset 35890
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 35858 . . 3 SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2 difss 4135 . . 3 ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
31, 2eqsstri 4029 . 2 SSet ⊆ (V × V)
4 df-rel 5691 . 2 (Rel SSet SSet ⊆ (V × V))
53, 4mpbir 231 1 Rel SSet
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3479  cdif 3947  wss 3950   E cep 5582   × cxp 5682  ran crn 5685  Rel wrel 5689  ctxp 35832   SSet csset 35834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-dif 3953  df-ss 3967  df-rel 5691  df-sset 35858
This theorem is referenced by:  brsset  35891  idsset  35892
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