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Mirrors > Home > HSE Home > Th. List > df-hvsub | Structured version Visualization version GIF version |
Description: Define vector subtraction. See hvsubvali 28803 for its value and hvsubcli 28804 for its closure. (Contributed by NM, 6-Jun-2008.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-hvsub | ⊢ −ℎ = (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 +ℎ (-1 ·ℎ 𝑦))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmv 28708 | . 2 class −ℎ | |
2 | vx | . . 3 setvar 𝑥 | |
3 | vy | . . 3 setvar 𝑦 | |
4 | chba 28702 | . . 3 class ℋ | |
5 | 2 | cv 1537 | . . . 4 class 𝑥 |
6 | c1 10527 | . . . . . 6 class 1 | |
7 | 6 | cneg 10860 | . . . . 5 class -1 |
8 | 3 | cv 1537 | . . . . 5 class 𝑦 |
9 | csm 28704 | . . . . 5 class ·ℎ | |
10 | 7, 8, 9 | co 7135 | . . . 4 class (-1 ·ℎ 𝑦) |
11 | cva 28703 | . . . 4 class +ℎ | |
12 | 5, 10, 11 | co 7135 | . . 3 class (𝑥 +ℎ (-1 ·ℎ 𝑦)) |
13 | 2, 3, 4, 4, 12 | cmpo 7137 | . 2 class (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 +ℎ (-1 ·ℎ 𝑦))) |
14 | 1, 13 | wceq 1538 | 1 wff −ℎ = (𝑥 ∈ ℋ, 𝑦 ∈ ℋ ↦ (𝑥 +ℎ (-1 ·ℎ 𝑦))) |
Colors of variables: wff setvar class |
This definition is referenced by: h2hvs 28760 hvsubf 28798 hvsubval 28799 |
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