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Definition df-hvsub 27956
Description: Define vector subtraction. See hvsubvali 28005 for its value and hvsubcli 28006 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 27910 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chil 27904 . . 3 class
52cv 1522 . . . 4 class 𝑥
6 c1 9975 . . . . . 6 class 1
76cneg 10305 . . . . 5 class -1
83cv 1522 . . . . 5 class 𝑦
9 csm 27906 . . . . 5 class ·
107, 8, 9co 6690 . . . 4 class (-1 · 𝑦)
11 cva 27905 . . . 4 class +
125, 10, 11co 6690 . . 3 class (𝑥 + (-1 · 𝑦))
132, 3, 4, 4, 12cmpt2 6692 . 2 class (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 + (-1 · 𝑦)))
141, 13wceq 1523 1 wff = (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 + (-1 · 𝑦)))
Colors of variables: wff setvar class
This definition is referenced by:  h2hvs  27962  hvsubf  28000  hvsubval  28001
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