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Theorem ollat 39195
Description: An ortholattice is a lattice. (Contributed by NM, 18-Sep-2011.)
Assertion
Ref Expression
ollat (𝐾 ∈ OL → 𝐾 ∈ Lat)

Proof of Theorem ollat
StepHypRef Expression
1 isolat 39194 . 2 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
21simplbi 497 1 (𝐾 ∈ OL → 𝐾 ∈ Lat)
Colors of variables: wff setvar class
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:  oldmm1  39199  oldmj1  39203  olj01  39207  olj02  39208  olm12  39210  latmassOLD  39211  latm12  39212  latm32  39213  latmrot  39214  latm4  39215  latmmdiN  39216  latmmdir  39217  olm01  39218  olm02  39219  omllat  39224  meetat  39278
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