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Theorem relsset 32588
 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 32556 . . 3 SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2 difss 3960 . . 3 ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
31, 2eqsstri 3854 . 2 SSet ⊆ (V × V)
4 df-rel 5364 . 2 (Rel SSet SSet ⊆ (V × V))
53, 4mpbir 223 1 Rel SSet
 Colors of variables: wff setvar class Syntax hints:  Vcvv 3398   ∖ cdif 3789   ⊆ wss 3792   E cep 5267   × cxp 5355  ran crn 5358  Rel wrel 5362   ⊗ ctxp 32530   SSet csset 32532 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-ext 2754 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-v 3400  df-dif 3795  df-in 3799  df-ss 3806  df-rel 5364  df-sset 32556 This theorem is referenced by:  brsset  32589  idsset  32590
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