Metamath Proof Explorer

Theorem chsleji

Description: Subspace sum is smaller than subspace join. Remark in Kalmbach p. 65. (Contributed by NM, 17-Oct-1999) (New usage is discouraged.)

Ref Expression
Hypotheses ch0le.1 
|- A e. CH
chjcl.2 
|- B e. CH
Assertion chsleji 
|- ( A +H B ) C_ ( A vH B )

Proof

Step Hyp Ref Expression
1 ch0le.1 
 |-  A e. CH
2 chjcl.2 
 |-  B e. CH
3 1 chshii 
 |-  A e. SH
4 2 chshii 
 |-  B e. SH
5 3 4 shsleji 
 |-  ( A +H B ) C_ ( A vH B )