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	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	chssii	$$⊢H\subseteq \mathscr{H}$$

Proof

Step	Hyp	Ref	Expression
1		chssi.1	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}$$
2	1	chshii	$$⊢H\in {\mathbf{S}}_{\mathscr{H}}$$
3	2	shssii	$$⊢H\subseteq \mathscr{H}$$