Users' Mathboxes Mathbox for Alexander van der Vekens < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-lindeps Structured version   Visualization version   GIF version

Definition df-lindeps 42761
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 42758 . 2 class linDepS
2 vs . . . . . 6 setvar 𝑠
32cv 1631 . . . . 5 class 𝑠
4 vm . . . . . 6 setvar 𝑚
54cv 1631 . . . . 5 class 𝑚
6 clininds 42757 . . . . 5 class linIndS
73, 5, 6wbr 4804 . . . 4 wff 𝑠 linIndS 𝑚
87wn 3 . . 3 wff ¬ 𝑠 linIndS 𝑚
98, 2, 4copab 4864 . 2 class {⟨𝑠, 𝑚⟩ ∣ ¬ 𝑠 linIndS 𝑚}
101, 9wceq 1632 1 wff linDepS = {⟨𝑠, 𝑚⟩ ∣ ¬ 𝑠 linIndS 𝑚}
Colors of variables: wff setvar class
This definition is referenced by:  lindepsnlininds  42769
  Copyright terms: Public domain W3C validator