Metamath Proof Explorer


Theorem ch0le

Description: The zero subspace is the smallest member of CH . (Contributed by NM, 14-Aug-2002) (New usage is discouraged.)

Ref Expression
Assertion ch0le
|- ( A e. CH -> 0H C_ A )

Proof

Step Hyp Ref Expression
1 chsh
 |-  ( A e. CH -> A e. SH )
2 sh0le
 |-  ( A e. SH -> 0H C_ A )
3 1 2 syl
 |-  ( A e. CH -> 0H C_ A )