Theorem olop 39196

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 39194	. 2 ⊢ (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
2	1	simprbi 496	1 ⊢ (𝐾 ∈ OL → 𝐾 ∈ OP)

Syntax hints:   → wi 4   ∈ wcel 2106  Latclat 18489  OPcops 39154  OLcol 39156

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-in 3970  df-ol 39160

This theorem is referenced by:  olposN  39197  oldmm1  39199  oldmm2  39200  oldmm3N  39201  oldmm4  39202  oldmj1  39203  oldmj2  39204  oldmj3  39205  oldmj4  39206  olj01  39207  olj02  39208  olm11  39209  olm12  39210  latmassOLD  39211  olm01  39218  olm02  39219  omlop  39223  meetat  39278  hlop  39344  polatN  39914