Description: A Hilbert lattice is an orthoposet. (Contributed by NM, 20-Oct-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | hlop | ⊢ ( 𝐾 ∈ HL → 𝐾 ∈ OP ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hlol | ⊢ ( 𝐾 ∈ HL → 𝐾 ∈ OL ) | |
2 | olop | ⊢ ( 𝐾 ∈ OL → 𝐾 ∈ OP ) | |
3 | 1 2 | syl | ⊢ ( 𝐾 ∈ HL → 𝐾 ∈ OP ) |