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Definition df-linds 20369
Description: An independent set is a set which is independent as a family. See also islinds3 20396 and islinds4 20397. (Contributed by Stefan O'Rear, 24-Feb-2015.)
Assertion
Ref Expression
df-linds LIndS = (𝑤 ∈ V ↦ {𝑠 ∈ 𝒫 (Base‘𝑤) ∣ ( I ↾ 𝑠) LIndF 𝑤})
Distinct variable group:   𝑤,𝑠

Detailed syntax breakdown of Definition df-linds
StepHypRef Expression
1 clinds 20367 . 2 class LIndS
2 vw . . 3 setvar 𝑤
3 cvv 3341 . . 3 class V
4 cid 5174 . . . . . 6 class I
5 vs . . . . . . 7 setvar 𝑠
65cv 1631 . . . . . 6 class 𝑠
74, 6cres 5269 . . . . 5 class ( I ↾ 𝑠)
82cv 1631 . . . . 5 class 𝑤
9 clindf 20366 . . . . 5 class LIndF
107, 8, 9wbr 4805 . . . 4 wff ( I ↾ 𝑠) LIndF 𝑤
11 cbs 16080 . . . . . 6 class Base
128, 11cfv 6050 . . . . 5 class (Base‘𝑤)
1312cpw 4303 . . . 4 class 𝒫 (Base‘𝑤)
1410, 5, 13crab 3055 . . 3 class {𝑠 ∈ 𝒫 (Base‘𝑤) ∣ ( I ↾ 𝑠) LIndF 𝑤}
152, 3, 14cmpt 4882 . 2 class (𝑤 ∈ V ↦ {𝑠 ∈ 𝒫 (Base‘𝑤) ∣ ( I ↾ 𝑠) LIndF 𝑤})
161, 15wceq 1632 1 wff LIndS = (𝑤 ∈ V ↦ {𝑠 ∈ 𝒫 (Base‘𝑤) ∣ ( I ↾ 𝑠) LIndF 𝑤})
Colors of variables: wff setvar class
This definition is referenced by:  islinds  20371
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