Theorem chss

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 )

Proof

Step	Hyp	Ref	Expression
1		chsh	⊢ ( 𝐻 ∈ Cℋ → 𝐻 ∈ Sℋ )
2		shss	⊢ ( 𝐻 ∈ Sℋ → 𝐻 ⊆ ℋ )
3	1 2	syl	⊢ ( 𝐻 ∈ Cℋ → 𝐻 ⊆ ℋ )