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Theorem ollat 38815
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 38814 . 2 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
21simplbi 496 1 (𝐾 ∈ OL → 𝐾 ∈ Lat)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  Latclat 18426  OPcops 38774  OLcol 38776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3463  df-in 3951  df-ol 38780
This theorem is referenced by:  oldmm1  38819  oldmj1  38823  olj01  38827  olj02  38828  olm12  38830  latmassOLD  38831  latm12  38832  latm32  38833  latmrot  38834  latm4  38835  latmmdiN  38836  latmmdir  38837  olm01  38838  olm02  38839  omllat  38844  meetat  38898
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