Theorem relsset 34235

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 34203	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4072	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 3960	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5607	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 230	1 ⊢ Rel SSet

Syntax hints:  Vcvv 3437   ∖ cdif 3889   ⊆ wss 3892   E cep 5505   × cxp 5598  ran crn 5601  Rel wrel 5605   ⊗ ctxp 34177   SSet csset 34179

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2707

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1542  df-ex 1780  df-sb 2066  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3439  df-dif 3895  df-in 3899  df-ss 3909  df-rel 5607  df-sset 34203

This theorem is referenced by:  brsset  34236  idsset  34237