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	⊢ 0ℋ ∈ Cℋ

Proof

Step	Hyp	Ref	Expression
1		df-ch0	⊢ 0ℋ = { 0ℎ }
2		hsn0elch	⊢ { 0ℎ } ∈ Cℋ
3	1 2	eqeltri	⊢ 0ℋ ∈ Cℋ