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Definition df-ind 26473
Description: Define the indicator function generator. (Contributed by Thierry Arnoux, 20-Jan-2017.)
Assertion
Ref Expression
df-ind  |- 𝟭  =  ( o  e.  _V  |->  ( a  e.  ~P o  |->  ( x  e.  o 
|->  if ( x  e.  a ,  1 ,  0 ) ) ) )
Distinct variable group:    o, a, x

Detailed syntax breakdown of Definition df-ind
StepHypRef Expression
1 cind 26472 . 2  class 𝟭
2 vo . . 3  setvar  o
3 cvv 2977 . . 3  class  _V
4 va . . . 4  setvar  a
52cv 1368 . . . . 5  class  o
65cpw 3865 . . . 4  class  ~P o
7 vx . . . . 5  setvar  x
87, 4wel 1757 . . . . . 6  wff  x  e.  a
9 c1 9288 . . . . . 6  class  1
10 cc0 9287 . . . . . 6  class  0
118, 9, 10cif 3796 . . . . 5  class  if ( x  e.  a ,  1 ,  0 )
127, 5, 11cmpt 4355 . . . 4  class  ( x  e.  o  |->  if ( x  e.  a ,  1 ,  0 ) )
134, 6, 12cmpt 4355 . . 3  class  ( a  e.  ~P o  |->  ( x  e.  o  |->  if ( x  e.  a ,  1 ,  0 ) ) )
142, 3, 13cmpt 4355 . 2  class  ( o  e.  _V  |->  ( a  e.  ~P o  |->  ( x  e.  o  |->  if ( x  e.  a ,  1 ,  0 ) ) ) )
151, 14wceq 1369 1  wff 𝟭  =  ( o  e.  _V  |->  ( a  e.  ~P o  |->  ( x  e.  o 
|->  if ( x  e.  a ,  1 ,  0 ) ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  indv  26474
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