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Definition df-lindeps 41521
Description: Define the relation between a module and its linearly dependent subsets. (Contributed by AV, 26-Apr-2019.)
Assertion
Ref Expression
df-lindeps linDepS = {⟨𝑠, 𝑚⟩ ∣ ¬ 𝑠 linIndS 𝑚}
Distinct variable group:   𝑚,𝑠

Detailed syntax breakdown of Definition df-lindeps
StepHypRef Expression
1 clindeps 41518 . 2 class linDepS
2 vs . . . . . 6 setvar 𝑠
32cv 1479 . . . . 5 class 𝑠
4 vm . . . . . 6 setvar 𝑚
54cv 1479 . . . . 5 class 𝑚
6 clininds 41517 . . . . 5 class linIndS
73, 5, 6wbr 4613 . . . 4 wff 𝑠 linIndS 𝑚
87wn 3 . . 3 wff ¬ 𝑠 linIndS 𝑚
98, 2, 4copab 4672 . 2 class {⟨𝑠, 𝑚⟩ ∣ ¬ 𝑠 linIndS 𝑚}
101, 9wceq 1480 1 wff linDepS = {⟨𝑠, 𝑚⟩ ∣ ¬ 𝑠 linIndS 𝑚}
Colors of variables: wff setvar class
This definition is referenced by:  lindepsnlininds  41529
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