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

Definition df-addr 41101
Description: Define the operation of vector addition. (Contributed by Andrew Salmon, 27-Jan-2012.)
Assertion
Ref Expression
df-addr +𝑟 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ ((𝑥𝑣) + (𝑦𝑣))))
Distinct variable group:   𝑥,𝑣,𝑦

Detailed syntax breakdown of Definition df-addr
StepHypRef Expression
1 cplusr 41095 . 2 class +𝑟
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cvv 3469 . . 3 class V
5 vv . . . 4 setvar 𝑣
6 cr 10525 . . . 4 class
75cv 1537 . . . . . 6 class 𝑣
82cv 1537 . . . . . 6 class 𝑥
97, 8cfv 6334 . . . . 5 class (𝑥𝑣)
103cv 1537 . . . . . 6 class 𝑦
117, 10cfv 6334 . . . . 5 class (𝑦𝑣)
12 caddc 10529 . . . . 5 class +
139, 11, 12co 7140 . . . 4 class ((𝑥𝑣) + (𝑦𝑣))
145, 6, 13cmpt 5122 . . 3 class (𝑣 ∈ ℝ ↦ ((𝑥𝑣) + (𝑦𝑣)))
152, 3, 4, 4, 14cmpo 7142 . 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:  addrval  41104
  Copyright terms: Public domain W3C validator