Theorem h0elch

Description: The zero subspace is a closed subspace. Part of Proposition 1 of Kalmbach p. 65. (Contributed by NM, 30-May-1999) (New usage is discouraged.)

	Ref	Expression
Assertion	h0elch	$$⊢0_{\mathscr{H}}\in {\mathbf{C}}_{\mathscr{H}}$$

Proof

Step	Hyp	Ref	Expression
1		df-ch0	$$⊢0_{\mathscr{H}}=\left\{0_{ℎ}\right\}$$
2		hsn0elch	$$⊢\left\{0_{ℎ}\right\}\in {\mathbf{C}}_{\mathscr{H}}$$
3	1 2	eqeltri	$$⊢0_{\mathscr{H}}\in {\mathbf{C}}_{\mathscr{H}}$$