Definition df-sn 3700

Description: Define the singleton of a class. Definition 7.1 of [Quine] p. 48. For convenience, it is well-defined for proper classes, i.e., those that are not elements of _V, although it is not very meaningful in this case. For an alternate definition see dfsn2 3708. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
df-sn	|- { A } = { x | x = A }

Distinct variable group:   x, A

Detailed syntax breakdown of Definition df-sn

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	csn 3694	. 2 class { A }
3		vx	. . . . 5 setvar x
4	3	cv 1397	. . . 4 class x
5	4, 1	wceq 1398	. . 3 wff x = A
6	5, 3	cab 2220	. 2 class { x | x = A }
7	2, 6	wceq 1398	1 wff { A } = { x | x = A }

This definition is referenced by:  sneq  3705  elsng  3709  csbsng  3755  rabsn  3761  pw0  3846  iunid  4052  dfiota2  5318  uniabio  5328  dfimafn2  5731  fnsnfv  5741  snec  6843  fngsum  13654  igsumvalx  13655  bdcsn  16779