Metamath Proof Explorer


Definition df-sn

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 , see snprc . For an alternate definition see dfsn2 . (Contributed by NM, 21-Jun-1993)

Ref Expression
Assertion df-sn A = x | x = A

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA class A
1 0 csn class A
2 vx setvar x
3 2 cv setvar x
4 3 0 wceq wff x = A
5 4 2 cab class x | x = A
6 1 5 wceq wff A = x | x = A