Theorem shssii

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	shssi.1	$$⊢H\in {\mathbf{S}}_{\mathscr{H}}$$
Assertion	shssii	$$⊢H\subseteq \mathscr{H}$$

Proof

Step	Hyp	Ref	Expression
1		shssi.1	$$⊢H\in {\mathbf{S}}_{\mathscr{H}}$$
2		shss	$$⊢H\in {\mathbf{S}}_{\mathscr{H}}\to H\subseteq \mathscr{H}$$
3	1 2	ax-mp	$$⊢H\subseteq \mathscr{H}$$