Definition df-css 19827

Description: Define set of closed subspaces. (Contributed by NM, 7-Oct-2011.)

Assertion

Ref	Expression
df-css	⊢ CSubSp = (ℎ ∈ V ↦ {𝑠 ∣ 𝑠 = ((ocv‘ℎ)‘((ocv‘ℎ)‘𝑠))})

Distinct variable group:   ℎ,𝑠

Detailed syntax breakdown of Definition df-css

Step	Hyp	Ref	Expression
1		ccss 19824	. 2 class CSubSp
2		vh	. . 3 setvar ℎ
3		cvv 3173	. . 3 class V
4		vs	. . . . . 6 setvar 𝑠
5	4	cv 1474	. . . . 5 class 𝑠
6	2	cv 1474	. . . . . . . 8 class ℎ
7		cocv 19823	. . . . . . . 8 class ocv
8	6, 7	cfv 5804	. . . . . . 7 class (ocv‘ℎ)
9	5, 8	cfv 5804	. . . . . 6 class ((ocv‘ℎ)‘𝑠)
10	9, 8	cfv 5804	. . . . 5 class ((ocv‘ℎ)‘((ocv‘ℎ)‘𝑠))
11	5, 10	wceq 1475	. . . 4 wff 𝑠 = ((ocv‘ℎ)‘((ocv‘ℎ)‘𝑠))
12	11, 4	cab 2596	. . 3 class {𝑠 ∣ 𝑠 = ((ocv‘ℎ)‘((ocv‘ℎ)‘𝑠))}
13	2, 3, 12	cmpt 4643	. 2 class (ℎ ∈ V ↦ {𝑠 ∣ 𝑠 = ((ocv‘ℎ)‘((ocv‘ℎ)‘𝑠))})
14	1, 13	wceq 1475	1 wff CSubSp = (ℎ ∈ V ↦ {𝑠 ∣ 𝑠 = ((ocv‘ℎ)‘((ocv‘ℎ)‘𝑠))})

This definition is referenced by:  cssval  19845