Metamath Proof Explorer

Theorem hlpos

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

Ref Expression
Assertion hlpos 
|- ( K e. HL -> K e. Poset )

Proof

Step Hyp Ref Expression
1 hllat 
 |-  ( K e. HL -> K e. Lat )
2 latpos 
 |-  ( K e. Lat -> K e. Poset )
3 1 2 syl 
 |-  ( K e. HL -> K e. Poset )