Theorem relsset 36336

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 36304	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4098	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 3991	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5672	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 234	1 ⊢ Rel SSet

Syntax hints:  Vcvv 3462   ∖ cdif 3910   ⊆ wss 3913   E cep 5564   × cxp 5663  ran crn 5666  Rel wrel 5670   ⊗ ctxp 36278   SSet csset 36280

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2152  ax-9 2160  ax-ext 2742

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1571  df-ex 1808  df-sb 2099  df-clab 2749  df-cleq 2762  df-clel 2845  df-v 3464  df-dif 3916  df-ss 3930  df-rel 5672  df-sset 36304

This theorem is referenced by:  brsset  36337  idsset  36338