Definition df-hvsub 28750

Description: Define vector subtraction. See hvsubvali 28799 for its value and hvsubcli 28800 for its closure. (Contributed by NM, 6-Jun-2008.) (New usage is discouraged.)

Assertion

Ref	Expression
df-hvsub	⊢ −ℎ = (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 +ℎ (-1 ·ℎ 𝑦)))

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-hvsub

Step	Hyp	Ref	Expression
1		cmv 28704	. 2 class −ℎ
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		chba 28698	. . 3 class ℋ
5	2	cv 1536	. . . 4 class 𝑥
6		c1 10540	. . . . . 6 class 1
7	6	cneg 10873	. . . . 5 class -1
8	3	cv 1536	. . . . 5 class 𝑦
9		csm 28700	. . . . 5 class ·ℎ
10	7, 8, 9	co 7158	. . . 4 class (-1 ·ℎ 𝑦)
11		cva 28699	. . . 4 class +ℎ
12	5, 10, 11	co 7158	. . 3 class (𝑥 +ℎ (-1 ·ℎ 𝑦))
13	2, 3, 4, 4, 12	cmpo 7160	. 2 class (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 +ℎ (-1 ·ℎ 𝑦)))
14	1, 13	wceq 1537	1 wff −ℎ = (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 +ℎ (-1 ·ℎ 𝑦)))

This definition is referenced by:  h2hvs  28756  hvsubf  28794  hvsubval  28795