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Definition df-subr 41004
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 40998 . 2 class -𝑟
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cvv 3479 . . 3 class V
5 vv . . . 4 setvar 𝑣
6 cr 10521 . . . 4 class
75cv 1537 . . . . . 6 class 𝑣
82cv 1537 . . . . . 6 class 𝑥
97, 8cfv 6336 . . . . 5 class (𝑥𝑣)
103cv 1537 . . . . . 6 class 𝑦
117, 10cfv 6336 . . . . 5 class (𝑦𝑣)
12 cmin 10855 . . . . 5 class
139, 11, 12co 7138 . . . 4 class ((𝑥𝑣) − (𝑦𝑣))
145, 6, 13cmpt 5127 . . 3 class (𝑣 ∈ ℝ ↦ ((𝑥𝑣) − (𝑦𝑣)))
152, 3, 4, 4, 14cmpo 7140 . 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ ((𝑥𝑣) − (𝑦𝑣))))
161, 15wceq 1538 1 wff -𝑟 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ ((𝑥𝑣) − (𝑦𝑣))))
Colors of variables: wff setvar class
This definition is referenced by:  subrval  41007
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