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Metamath Proof Explorer

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	$⊢ 0_{ℋ} \in C_{ℋ}$

Proof

Step	Hyp	Ref	Expression
1		df-ch0	$⊢ 0_{ℋ} = \{0_{ℎ}\}$
2		hsn0elch	$⊢ \{0_{ℎ}\} \in C_{ℋ}$
3	1 2	eqeltri	$⊢ 0_{ℋ} \in C_{ℋ}$