Definition df-singleton 31969

Description: Define the singleton function. See brsingle 32024 for its value. (Contributed by Scott Fenton, 4-Apr-2014.)

Assertion

Ref	Expression
df-singleton	|- Singleton = ( ( _V X. _V ) \ ran ( ( _V (x) _E ) /_\ ( _I (x) _V ) ) )

Detailed syntax breakdown of Definition df-singleton

Step	Hyp	Ref	Expression
1		csingle 31945	. 2 class Singleton
2		cvv 3200	. . . 4 class _V
3	2, 2	cxp 5112	. . 3 class ( _V X. _V )
4		cep 5028	. . . . . 6 class _E
5	2, 4	ctxp 31937	. . . . 5 class ( _V (x) _E )
6		cid 5023	. . . . . 6 class _I
7	6, 2	ctxp 31937	. . . . 5 class ( _I (x) _V )
8	5, 7	csymdif 3843	. . . 4 class ( ( _V (x) _E ) /_\ ( _I (x) _V ) )
9	8	crn 5115	. . 3 class ran ( ( _V (x) _E ) /_\ ( _I (x) _V ) )
10	3, 9	cdif 3571	. 2 class ( ( _V X. _V ) \ ran ( ( _V (x) _E ) /_\ ( _I (x) _V ) ) )
11	1, 10	wceq 1483	1 wff Singleton = ( ( _V X. _V ) \ ran ( ( _V (x) _E ) /_\ ( _I (x) _V ) ) )

This definition is referenced by:  brsingle  32024  fnsingle  32026