Theorem relsset 36572

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 36540	. . 3 ⊢ SSet = ((V × V) ∖ ran ( E ⊗ (V ∖ E )))
2		difss 4082	. . 3 ⊢ ((V × V) ∖ ran ( E ⊗ (V ∖ E ))) ⊆ (V × V)
3	1, 2	eqsstri 3976	. 2 ⊢ SSet ⊆ (V × V)
4		df-rel 5654	. 2 ⊢ (Rel SSet ↔ SSet ⊆ (V × V))
5	3, 4	mpbir 234	1 ⊢ Rel SSet

This proof depends on syntax axioms:  Vcvv 3450   ∖ cdif 3895   ⊆ wss 3898   E cep 5546   × cxp 5645  ran crn 5648  Rel wrel 5652   ⊗ ctxp 36514   SSet csset 36516

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-dif 3901  df-ss 3915  df-rel 5654  df-sset 36540

This theorem is used by:  brsset  36573  idsset  36574