Theorem relsset 36123

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 36091	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4067	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 3961	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5626	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 232	1 ⊢ Rel SSet

Syntax hints:  Vcvv 3431   ∖ cdif 3880   ⊆ wss 3883   E cep 5518   × cxp 5617  ran crn 5620  Rel wrel 5624   ⊗ ctxp 36065   SSet csset 36067

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-dif 3886  df-ss 3900  df-rel 5626  df-sset 36091

This theorem is referenced by:  brsset  36124  idsset  36125