Description: A closed subspace of a Hilbert space is a subset of Hilbert space. (Contributed by NM, 24-Aug-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | chss | ⊢ ( 𝐻 ∈ Cℋ → 𝐻 ⊆ ℋ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chsh | ⊢ ( 𝐻 ∈ Cℋ → 𝐻 ∈ Sℋ ) | |
2 | shss | ⊢ ( 𝐻 ∈ Sℋ → 𝐻 ⊆ ℋ ) | |
3 | 1 2 | syl | ⊢ ( 𝐻 ∈ Cℋ → 𝐻 ⊆ ℋ ) |