Description: A closed subspace of a Hilbert space is a subset of Hilbert space. (Contributed by NM, 6-Oct-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | shssi.1 | ⊢ 𝐻 ∈ Sℋ | |
Assertion | shssii | ⊢ 𝐻 ⊆ ℋ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | shssi.1 | ⊢ 𝐻 ∈ Sℋ | |
2 | shss | ⊢ ( 𝐻 ∈ Sℋ → 𝐻 ⊆ ℋ ) | |
3 | 1 2 | ax-mp | ⊢ 𝐻 ⊆ ℋ |