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Metamath Proof Explorer

Theorem hlop

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

Ref Expression
Assertion hlop 
|- ( K e. HL -> K e. OP )

Proof

Step Hyp Ref Expression
1 hlol 
 |-  ( K e. HL -> K e. OL )
2 olop 
 |-  ( K e. OL -> K e. OP )
3 1 2 syl 
 |-  ( K e. HL -> K e. OP )