Metamath Proof Explorer

Theorem hlol

Description: A Hilbert lattice is an ortholattice. (Contributed by NM, 20-Oct-2011)

Ref Expression
Assertion hlol 
|- ( K e. HL -> K e. OL )

Proof

Step Hyp Ref Expression
1 hloml 
 |-  ( K e. HL -> K e. OML )
2 omlol 
 |-  ( K e. OML -> K e. OL )
3 1 2 syl 
 |-  ( K e. HL -> K e. OL )