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Definition df-hvsub 27001
Description: Define vector subtraction. See hvsubvali 27050 for its value and hvsubcli 27051 for its closure. (Contributed by NM, 6-Jun-2008.) (New usage is discouraged.)
Assertion
Ref Expression
df-hvsub = (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 + (-1 · 𝑦)))
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-hvsub
StepHypRef Expression
1 cmv 26955 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chil 26949 . . 3 class
52cv 1473 . . . 4 class 𝑥
6 c1 9691 . . . . . 6 class 1
76cneg 10017 . . . . 5 class -1
83cv 1473 . . . . 5 class 𝑦
9 csm 26951 . . . . 5 class ·
107, 8, 9co 6425 . . . 4 class (-1 · 𝑦)
11 cva 26950 . . . 4 class +
125, 10, 11co 6425 . . 3 class (𝑥 + (-1 · 𝑦))
132, 3, 4, 4, 12cmpt2 6427 . 2 class (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 + (-1 · 𝑦)))
141, 13wceq 1474 1 wff = (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 + (-1 · 𝑦)))
Colors of variables: wff setvar class
This definition is referenced by:  h2hvs  27007  hvsubf  27045  hvsubval  27046
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