Theorem chssii

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	chssi.1	⊢ 𝐻 ∈ Cℋ
Assertion	chssii	⊢ 𝐻 ⊆ ℋ

Proof

Step	Hyp	Ref	Expression
1		chssi.1	⊢ 𝐻 ∈ Cℋ
2	1	chshii	⊢ 𝐻 ∈ Sℋ
3	2	shssii	⊢ 𝐻 ⊆ ℋ