Description: A Hilbert lattice is a poset. (Contributed by NM, 20-Oct-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | hlpos | ⊢ ( 𝐾 ∈ HL → 𝐾 ∈ Poset ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hllat | ⊢ ( 𝐾 ∈ HL → 𝐾 ∈ Lat ) | |
2 | latpos | ⊢ ( 𝐾 ∈ Lat → 𝐾 ∈ Poset ) | |
3 | 1 2 | syl | ⊢ ( 𝐾 ∈ HL → 𝐾 ∈ Poset ) |