Metamath Proof Explorer
Description: The span of a singleton in Hilbert space is a closed subspace.
(Contributed by NM, 3-Jun-2004) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypothesis |
spansnch.1 |
⊢ 𝐴 ∈ ℋ |
|
Assertion |
spansnchi |
⊢ ( span ‘ { 𝐴 } ) ∈ Cℋ |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
spansnch.1 |
⊢ 𝐴 ∈ ℋ |
2 |
|
spansnch |
⊢ ( 𝐴 ∈ ℋ → ( span ‘ { 𝐴 } ) ∈ Cℋ ) |
3 |
1 2
|
ax-mp |
⊢ ( span ‘ { 𝐴 } ) ∈ Cℋ |