Mathbox for Andrew Salmon < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-subr Structured version   Visualization version   GIF version

Definition df-subr 38488
 Description: Define the operation of vector subtraction. (Contributed by Andrew Salmon, 27-Jan-2012.)
Assertion
Ref Expression
df-subr -𝑟 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ ((𝑥𝑣) − (𝑦𝑣))))
Distinct variable group:   𝑥,𝑣,𝑦

Detailed syntax breakdown of Definition df-subr
StepHypRef Expression
1 cminusr 38482 . 2 class -𝑟
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cvv 3195 . . 3 class V
5 vv . . . 4 setvar 𝑣
6 cr 9920 . . . 4 class
75cv 1480 . . . . . 6 class 𝑣
82cv 1480 . . . . . 6 class 𝑥
97, 8cfv 5876 . . . . 5 class (𝑥𝑣)
103cv 1480 . . . . . 6 class 𝑦
117, 10cfv 5876 . . . . 5 class (𝑦𝑣)
12 cmin 10251 . . . . 5 class
139, 11, 12co 6635 . . . 4 class ((𝑥𝑣) − (𝑦𝑣))
145, 6, 13cmpt 4720 . . 3 class (𝑣 ∈ ℝ ↦ ((𝑥𝑣) − (𝑦𝑣)))
152, 3, 4, 4, 14cmpt2 6637 . 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ ((𝑥𝑣) − (𝑦𝑣))))
161, 15wceq 1481 1 wff -𝑟 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ ((𝑥𝑣) − (𝑦𝑣))))
 Colors of variables: wff setvar class This definition is referenced by:  subrval  38491
 Copyright terms: Public domain W3C validator