Theorem relsset 36002

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 35970	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4085	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 3977	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5628	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 231	1 ⊢ Rel SSet

Syntax hints:  Vcvv 3437   ∖ cdif 3895   ⊆ wss 3898   E cep 5520   × cxp 5619  ran crn 5622  Rel wrel 5626   ⊗ ctxp 35944   SSet csset 35946

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-v 3439  df-dif 3901  df-ss 3915  df-rel 5628  df-sset 35970

This theorem is referenced by:  brsset  36003  idsset  36004