Definition df-ind 32833

Description: Define the indicator function generator. (Contributed by Thierry Arnoux, 20-Jan-2017.)

Assertion

Ref	Expression
df-ind	⊢ 𝟭 = (𝑜 ∈ V ↦ (𝑎 ∈ 𝒫 𝑜 ↦ (𝑥 ∈ 𝑜 ↦ if(𝑥 ∈ 𝑎, 1, 0))))

Distinct variable group:   𝑜,𝑎,𝑥

Detailed syntax breakdown of Definition df-ind

Step	Hyp	Ref	Expression
1		cind 32832	. 2 class 𝟭
2		vo	. . 3 setvar 𝑜
3		cvv 3464	. . 3 class V
4		va	. . . 4 setvar 𝑎
5	2	cv 1539	. . . . 5 class 𝑜
6	5	cpw 4580	. . . 4 class 𝒫 𝑜
7		vx	. . . . 5 setvar 𝑥
8	7, 4	wel 2110	. . . . . 6 wff 𝑥 ∈ 𝑎
9		c1 11135	. . . . . 6 class 1
10		cc0 11134	. . . . . 6 class 0
11	8, 9, 10	cif 4505	. . . . 5 class if(𝑥 ∈ 𝑎, 1, 0)
12	7, 5, 11	cmpt 5206	. . . 4 class (𝑥 ∈ 𝑜 ↦ if(𝑥 ∈ 𝑎, 1, 0))
13	4, 6, 12	cmpt 5206	. . 3 class (𝑎 ∈ 𝒫 𝑜 ↦ (𝑥 ∈ 𝑜 ↦ if(𝑥 ∈ 𝑎, 1, 0)))
14	2, 3, 13	cmpt 5206	. 2 class (𝑜 ∈ V ↦ (𝑎 ∈ 𝒫 𝑜 ↦ (𝑥 ∈ 𝑜 ↦ if(𝑥 ∈ 𝑎, 1, 0))))
15	1, 14	wceq 1540	1 wff 𝟭 = (𝑜 ∈ V ↦ (𝑎 ∈ 𝒫 𝑜 ↦ (𝑥 ∈ 𝑜 ↦ if(𝑥 ∈ 𝑎, 1, 0))))

This definition is referenced by:  indv  32834