Definition df-sn 3373

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 3381. (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 3367	. 2 class {A }
3		vx	. . . . 5 setvar x
4	3	cv 1241	. . . 4 class x
5	4, 1	wceq 1242	. . 3 wff x = A
6	5, 3	cab 2023	. 2 class {x | x = A }
7	2, 6	wceq 1242	1 wff {A } = {x | x = A }

This definition is referenced by:  sneq  3378  elsn  3382  elsncg  3389  csbsng  3422  rabsn  3428  pw0  3502  iunid  3703  dfiota2  4811  uniabio  4820  dfimafn2  5166  fnsnfv  5175  snec  6103  bdcsn  9259