Theorem relsset 34849

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 34817	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4131	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 4016	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5683	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 230	1 ⊢ Rel SSet

Syntax hints:  Vcvv 3475   ∖ cdif 3945   ⊆ wss 3948   E cep 5579   × cxp 5674  ran crn 5677  Rel wrel 5681   ⊗ ctxp 34791   SSet csset 34793

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-dif 3951  df-in 3955  df-ss 3965  df-rel 5683  df-sset 34817

This theorem is referenced by:  brsset  34850  idsset  34851