Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-singleton Structured version   Unicode version

Definition df-singleton 25706
Description: Define the singleton function. See brsingle 25762 for its value. (Contributed by Scott Fenton, 4-Apr-2014.)
Assertion
Ref Expression
df-singleton  |- Singleton  =  ( ( _V  X.  _V )  \  ran  ( ( _V  (x)  _E  )(++) (  _I  (x)  _V )
) )

Detailed syntax breakdown of Definition df-singleton
StepHypRef Expression
1 csingle 25682 . 2  class Singleton
2 cvv 2956 . . . 4  class  _V
32, 2cxp 4876 . . 3  class  ( _V 
X.  _V )
4 cep 4492 . . . . . 6  class  _E
52, 4ctxp 25674 . . . . 5  class  ( _V 
(x)  _E  )
6 cid 4493 . . . . . 6  class  _I
76, 2ctxp 25674 . . . . 5  class  (  _I 
(x)  _V )
85, 7csymdif 25662 . . . 4  class  ( ( _V  (x)  _E  )(++) (  _I  (x)  _V )
)
98crn 4879 . . 3  class  ran  (
( _V  (x)  _E  )(++) (  _I  (x)  _V ) )
103, 9cdif 3317 . 2  class  ( ( _V  X.  _V )  \  ran  ( ( _V 
(x)  _E  )(++) (  _I  (x)  _V ) ) )
111, 10wceq 1652 1  wff Singleton  =  ( ( _V  X.  _V )  \  ran  ( ( _V  (x)  _E  )(++) (  _I  (x)  _V )
) )
Colors of variables: wff set class
This definition is referenced by:  brsingle  25762  fnsingle  25764
  Copyright terms: Public domain W3C validator