Theorem chshii

Description: A closed subspace is a subspace. (Contributed by NM, 19-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Hypothesis	chshi.1	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	chshii	$$⊢H\in {\mathbf{S}}_{\mathscr{H}}$$

Proof

Step	Hyp	Ref	Expression
1		chshi.1	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}$$
2		chsh	$$⊢H\in {\mathbf{C}}_{\mathscr{H}}\to H\in {\mathbf{S}}_{\mathscr{H}}$$
3	1 2	ax-mp	$$⊢H\in {\mathbf{S}}_{\mathscr{H}}$$