Theorem relsset 35870

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

Step	Hyp	Ref	Expression
1		df-sset 35838	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4146	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 4030	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5696	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 231	1 ⊢ Rel SSet

Syntax hints:  Vcvv 3478   ∖ cdif 3960   ⊆ wss 3963   E cep 5588   × cxp 5687  ran crn 5690  Rel wrel 5694   ⊗ ctxp 35812   SSet csset 35814

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-dif 3966  df-ss 3980  df-rel 5696  df-sset 35838

This theorem is referenced by:  brsset  35871  idsset  35872