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 
|- 0H e. CH

Proof

Step Hyp Ref Expression
1 df-ch0 
 |-  0H = { 0h }
2 hsn0elch 
 |-  { 0h } e. CH
3 1 2 eqeltri 
 |-  0H e. CH