Theorem relsset 35876

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 35844	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4099	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 3993	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5645	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 231	1 ⊢ Rel SSet

Syntax hints:  Vcvv 3447   ∖ cdif 3911   ⊆ wss 3914   E cep 5537   × cxp 5636  ran crn 5639  Rel wrel 5643   ⊗ ctxp 35818   SSet csset 35820

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 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-dif 3917  df-ss 3931  df-rel 5645  df-sset 35844

This theorem is referenced by:  brsset  35877  idsset  35878