Theorem relsset 36386

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 36354	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4089	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 3982	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5667	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 234	1 ⊢ Rel SSet

This proof depends on syntax axioms:  Vcvv 3454   ∖ cdif 3901   ⊆ wss 3904   E cep 5559   × cxp 5658  ran crn 5661  Rel wrel 5665   ⊗ ctxp 36328   SSet csset 36330

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-dif 3907  df-ss 3921  df-rel 5667  df-sset 36354

This theorem is used by:  brsset  36387  idsset  36388