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Metamath Proof Explorer
Description: Scalar multiplication by one. (Contributed by NM, 30-May-1999)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
ax-hvmulid |
⊢ ( 𝐴 ∈ ℋ → ( 1 ·ℎ 𝐴 ) = 𝐴 ) |
Detailed syntax breakdown
| Step |
Hyp |
Ref |
Expression |
| 0 |
|
cA |
⊢ 𝐴 |
| 1 |
|
chba |
⊢ ℋ |
| 2 |
0 1
|
wcel |
⊢ 𝐴 ∈ ℋ |
| 3 |
|
c1 |
⊢ 1 |
| 4 |
|
csm |
⊢ ·ℎ |
| 5 |
3 0 4
|
co |
⊢ ( 1 ·ℎ 𝐴 ) |
| 6 |
5 0
|
wceq |
⊢ ( 1 ·ℎ 𝐴 ) = 𝐴 |
| 7 |
2 6
|
wi |
⊢ ( 𝐴 ∈ ℋ → ( 1 ·ℎ 𝐴 ) = 𝐴 ) |