Definition df-ind 9294

Description: Define the indicator function generator. It generates an indicator function ( (𝟭 ` O ) ` A ) for a given domain O and a given subset A of the domain, see indval 9296. In contrast to the definitions and notations in Wikipedia and [Lang2] p. 3, the domain and the subset are always mentioned explicitly. (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

Step	Hyp	Ref	Expression
1		cind 9293	. 2 class 𝟭
2		vo	. . 3 setvar o
3		cvv 2821	. . 3 class _V
4		va	. . . 4 setvar a
5	2	cv 1401	. . . . 5 class o
6	5	cpw 3688	. . . 4 class ~P o
7		vx	. . . . 5 setvar x
8	7, 4	wel 2210	. . . . . 6 wff x e. a
9		c1 8180	. . . . . 6 class 1
10		cc0 8179	. . . . . 6 class 0
11	8, 9, 10	cif 3638	. . . . 5 class if ( x e. a , 1 , 0 )
12	7, 5, 11	cmpt 4192	. . . 4 class ( x e. o |-> if ( x e. a , 1 , 0 ) )
13	4, 6, 12	cmpt 4192	. . 3 class ( a e. ~P o |-> ( x e. o |-> if ( x e. a , 1 , 0 ) ) )
14	2, 3, 13	cmpt 4192	. 2 class ( o e. _V |-> ( a e. ~P o |-> ( x e. o |-> if ( x e. a , 1 , 0 ) ) ) )
15	1, 14	wceq 1402	1 wff 𝟭 = ( o e. _V |-> ( a e. ~P o |-> ( x e. o |-> if ( x e. a , 1 , 0 ) ) ) )

This definition is used by:  indv  9295  indval0  9297