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Definition df-hvsub 28757
Description: Define vector subtraction. See hvsubvali 28806 for its value and hvsubcli 28807 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 28711 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chba 28705 . . 3 class
52cv 1537 . . . 4 class 𝑥
6 c1 10536 . . . . . 6 class 1
76cneg 10869 . . . . 5 class -1
83cv 1537 . . . . 5 class 𝑦
9 csm 28707 . . . . 5 class ·
107, 8, 9co 7149 . . . 4 class (-1 · 𝑦)
11 cva 28706 . . . 4 class +
125, 10, 11co 7149 . . 3 class (𝑥 + (-1 · 𝑦))
132, 3, 4, 4, 12cmpo 7151 . 2 class (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 + (-1 · 𝑦)))
141, 13wceq 1538 1 wff = (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 + (-1 · 𝑦)))
Colors of variables: wff setvar class
This definition is referenced by:  h2hvs  28763  hvsubf  28801  hvsubval  28802
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