Metamath Proof Explorer

Definition df-sset

Description: Define the subset class. For the value, see brsset . (Contributed by Scott Fenton, 31-Mar-2012)

Ref Expression
Assertion df-sset 
|- SSet = ( ( _V X. _V ) \ ran ( _E (x) ( _V \ _E ) ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 csset 
 |-  SSet
1 cvv 
 |-  _V
2 1 1 cxp 
 |-  ( _V X. _V )
3 cep 
 |-  _E
4 1 3 cdif 
 |-  ( _V \ _E )
5 3 4 ctxp 
 |-  ( _E (x) ( _V \ _E ) )
6 5 crn 
 |-  ran ( _E (x) ( _V \ _E ) )
7 2 6 cdif 
 |-  ( ( _V X. _V ) \ ran ( _E (x) ( _V \ _E ) ) )
8 0 7 wceq 
 |-  SSet = ( ( _V X. _V ) \ ran ( _E (x) ( _V \ _E ) ) )