Theorem chsssh

Description: Closed subspaces are subspaces in a Hilbert space. (Contributed by NM, 29-May-1999) (Revised by Mario Carneiro, 23-Dec-2013) (New usage is discouraged.)

	Ref	Expression
Assertion	chsssh	⊢ Cℋ ⊆ Sℋ

Proof

Step	Hyp	Ref	Expression
1		chsh	⊢ ( 𝑥 ∈ Cℋ → 𝑥 ∈ Sℋ )
2	1	ssriv	⊢ Cℋ ⊆ Sℋ