Theorem chsspwh

Description: Closed subspaces are subsets of Hilbert space. (Contributed by NM, 24-Nov-2004) (New usage is discouraged.)

	Ref	Expression
Assertion	chsspwh	⊢ Cℋ ⊆ 𝒫 ℋ

Proof

Step	Hyp	Ref	Expression
1		chsssh	⊢ Cℋ ⊆ Sℋ
2		shsspwh	⊢ Sℋ ⊆ 𝒫 ℋ
3	1 2	sstri	⊢ Cℋ ⊆ 𝒫 ℋ