ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-sn Unicode version

Definition df-sn 3408
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 3416. (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 3402 . 2  class  { A }
3 vx . . . . 5  setvar  x
43cv 1258 . . . 4  class  x
54, 1wceq 1259 . . 3  wff  x  =  A
65, 3cab 2042 . 2  class  { x  |  x  =  A }
72, 6wceq 1259 1  wff  { A }  =  { x  |  x  =  A }
Colors of variables: wff set class
This definition is referenced by:  sneq  3413  elsng  3417  csbsng  3458  rabsn  3464  pw0  3538  iunid  3739  dfiota2  4895  uniabio  4904  dfimafn2  5250  fnsnfv  5259  snec  6197  bdcsn  10363
  Copyright terms: Public domain W3C validator