Metamath Proof Explorer


Theorem omlop

Description: An orthomodular lattice is an orthoposet. (Contributed by NM, 6-Nov-2011)

Ref Expression
Assertion omlop ( 𝐾 ∈ OML → 𝐾 ∈ OP )

Proof

Step Hyp Ref Expression
1 omlol ( 𝐾 ∈ OML → 𝐾 ∈ OL )
2 olop ( 𝐾 ∈ OL → 𝐾 ∈ OP )
3 1 2 syl ( 𝐾 ∈ OML → 𝐾 ∈ OP )