Theorem relsset 34169

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 34137	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4070	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 3959	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5595	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 230	1 ⊢ Rel SSet

Syntax hints:  Vcvv 3430   ∖ cdif 3888   ⊆ wss 3891   E cep 5493   × cxp 5586  ran crn 5589  Rel wrel 5593   ⊗ ctxp 34111   SSet csset 34113

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1801  ax-4 1815  ax-5 1916  ax-6 1974  ax-7 2014  ax-8 2111  ax-9 2119  ax-ext 2710

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1544  df-ex 1786  df-sb 2071  df-clab 2717  df-cleq 2731  df-clel 2817  df-v 3432  df-dif 3894  df-in 3898  df-ss 3908  df-rel 5595  df-sset 34137

This theorem is referenced by:  brsset  34170  idsset  34171