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Definition df-css 20726
Description: Define the set of closed (linear) subspaces of a given pre-Hilbert space. (Contributed by NM, 7-Oct-2011.)
Assertion
Ref Expression
df-css ClSubSp = ( ∈ V ↦ {𝑠𝑠 = ((ocv‘)‘((ocv‘)‘𝑠))})
Distinct variable group:   ,𝑠

Detailed syntax breakdown of Definition df-css
StepHypRef Expression
1 ccss 20723 . 2 class ClSubSp
2 vh . . 3 setvar
3 cvv 3499 . . 3 class V
4 vs . . . . . 6 setvar 𝑠
54cv 1529 . . . . 5 class 𝑠
62cv 1529 . . . . . . . 8 class
7 cocv 20722 . . . . . . . 8 class ocv
86, 7cfv 6351 . . . . . . 7 class (ocv‘)
95, 8cfv 6351 . . . . . 6 class ((ocv‘)‘𝑠)
109, 8cfv 6351 . . . . 5 class ((ocv‘)‘((ocv‘)‘𝑠))
115, 10wceq 1530 . . . 4 wff 𝑠 = ((ocv‘)‘((ocv‘)‘𝑠))
1211, 4cab 2803 . . 3 class {𝑠𝑠 = ((ocv‘)‘((ocv‘)‘𝑠))}
132, 3, 12cmpt 5142 . 2 class ( ∈ V ↦ {𝑠𝑠 = ((ocv‘)‘((ocv‘)‘𝑠))})
141, 13wceq 1530 1 wff ClSubSp = ( ∈ V ↦ {𝑠𝑠 = ((ocv‘)‘((ocv‘)‘𝑠))})
Colors of variables: wff setvar class
This definition is referenced by:  cssval  20744
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