This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Addition with the zero vector. (Contributed by NM, 16-Aug-1999)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
ax-hvaddid |
⊢ ( 𝐴 ∈ ℋ → ( 𝐴 +ℎ 0ℎ ) = 𝐴 ) |
Detailed syntax breakdown
| Step |
Hyp |
Ref |
Expression |
| 0 |
|
cA |
⊢ 𝐴 |
| 1 |
|
chba |
⊢ ℋ |
| 2 |
0 1
|
wcel |
⊢ 𝐴 ∈ ℋ |
| 3 |
|
cva |
⊢ +ℎ |
| 4 |
|
c0v |
⊢ 0ℎ |
| 5 |
0 4 3
|
co |
⊢ ( 𝐴 +ℎ 0ℎ ) |
| 6 |
5 0
|
wceq |
⊢ ( 𝐴 +ℎ 0ℎ ) = 𝐴 |
| 7 |
2 6
|
wi |
⊢ ( 𝐴 ∈ ℋ → ( 𝐴 +ℎ 0ℎ ) = 𝐴 ) |