Definition df-scan 6327

Description: Define the class of strongly Cantorian sets. Unlike general Cantorian sets, this fixes a specific mapping between x and ℘₁x. Definition from [Holmes] p. 134. (Contributed by Scott Fenton, 19-Apr-2021.)

Assertion

Ref	Expression
df-scan	⊢ SCan = {x ∣ (y ∈ x ↦ {y}) ∈ V}

Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-scan

Step	Hyp	Ref	Expression
1		cscan 6326	. 2 class SCan
2		vy	. . . . 5 setvar y
3		vx	. . . . . 6 setvar x
4	3	cv 1641	. . . . 5 class x
5	2	cv 1641	. . . . . 6 class y
6	5	csn 3738	. . . . 5 class {y}
7	2, 4, 6	cmpt 5652	. . . 4 class (y ∈ x ↦ {y})
8		cvv 2860	. . . 4 class V
9	7, 8	wcel 1710	. . 3 wff (y ∈ x ↦ {y}) ∈ V
10	9, 3	cab 2339	. 2 class {x ∣ (y ∈ x ↦ {y}) ∈ V}
11	1, 10	wceq 1642	1 wff SCan = {x ∣ (y ∈ x ↦ {y}) ∈ V}

This definition is referenced by:  elscan  6331