Definition df-sn 3714

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 3722. (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 3708	. 2 class { A }
3		vx	. . . . 5 setvar x
4	3	cv 1401	. . . 4 class x
5	4, 1	wceq 1402	. . 3 wff x = A
6	5, 3	cab 2224	. 2 class { x | x = A }
7	2, 6	wceq 1402	1 wff { A } = { x | x = A }

This definition is referenced by:  sneq  3719  elsng  3723  csbsng  3769  rabsn  3775  pw0  3860  iunid  4066  dfiota2  5336  uniabio  5346  dfimafn2  5749  fnsnfv  5759  snec  6864  fset0  6943  fngzsum  13691  gzsumvalx  13692  bdcsn  16879