This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem hlatl

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

Ref Expression
Assertion hlatl 
|- ( K e. HL -> K e. AtLat )

Proof

Step Hyp Ref Expression
1 hlcvl 
 |-  ( K e. HL -> K e. CvLat )
2 cvlatl 
 |-  ( K e. CvLat -> K e. AtLat )
3 1 2 syl 
 |-  ( K e. HL -> K e. AtLat )