Metamath Proof Explorer

Theorem hllat

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

Ref Expression
Assertion hllat 
|- ( K e. HL -> K e. Lat )

Proof

Step Hyp Ref Expression
1 hlatl 
 |-  ( K e. HL -> K e. AtLat )
2 atllat 
 |-  ( K e. AtLat -> K e. Lat )
3 1 2 syl 
 |-  ( K e. HL -> K e. Lat )