Theorem h0elsh

Description: The zero subspace is a subspace of Hilbert space. (Contributed by NM, 2-Jun-2004) (New usage is discouraged.)

	Ref	Expression
Assertion	h0elsh	$$⊢0_{\mathscr{H}}\in {\mathbf{S}}_{\mathscr{H}}$$

Proof

Step	Hyp	Ref	Expression
1		h0elch	$$⊢0_{\mathscr{H}}\in {\mathbf{C}}_{\mathscr{H}}$$
2	1	chshii	$$⊢0_{\mathscr{H}}\in {\mathbf{S}}_{\mathscr{H}}$$