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Definition df-sn 3437
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 3445. (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
StepHypRef Expression
1 cA . . 3  class  A
21csn 3431 . 2  class  { A }
3 vx . . . . 5  setvar  x
43cv 1286 . . . 4  class  x
54, 1wceq 1287 . . 3  wff  x  =  A
65, 3cab 2071 . 2  class  { x  |  x  =  A }
72, 6wceq 1287 1  wff  { A }  =  { x  |  x  =  A }
Colors of variables: wff set class
This definition is referenced by:  sneq  3442  elsng  3446  csbsng  3488  rabsn  3494  pw0  3569  iunid  3770  dfiota2  4949  uniabio  4958  dfimafn2  5319  fnsnfv  5328  snec  6307  bdcsn  11230
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