Theorem olop 38079

Description: An ortholattice is an orthoposet. (Contributed by NM, 18-Sep-2011.)

Assertion

Ref	Expression
olop	⊢ (𝐾 ∈ OL → 𝐾 ∈ OP)

Proof of Theorem olop

Step	Hyp	Ref	Expression
1		isolat 38077	. 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
2	1	simprbi 497	1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ OP)

Syntax hints:   → wi 4   ∈ wcel 2106  Latclat 18383  OPcops 38037  OLcol 38039

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-in 3955  df-ol 38043

This theorem is referenced by:  olposN  38080  oldmm1  38082  oldmm2  38083  oldmm3N  38084  oldmm4  38085  oldmj1  38086  oldmj2  38087  oldmj3  38088  oldmj4  38089  olj01  38090  olj02  38091  olm11  38092  olm12  38093  latmassOLD  38094  olm01  38101  olm02  38102  omlop  38106  meetat  38161  hlop  38227  polatN  38797