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	$$⊢{\mathbf{C}}_{\mathscr{H}}\subseteq {\mathbf{S}}_{\mathscr{H}}$$

Proof

Step	Hyp	Ref	Expression
1		chsh	$$⊢x\in {\mathbf{C}}_{\mathscr{H}}\to x\in {\mathbf{S}}_{\mathscr{H}}$$
2	1	ssriv	$$⊢{\mathbf{C}}_{\mathscr{H}}\subseteq {\mathbf{S}}_{\mathscr{H}}$$