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 0C

Proof

Step Hyp Ref Expression
1 df-ch0 0 = { 0 }
2 hsn0elch { 0 } ∈ C
3 1 2 eqeltri 0C