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Theorem ollat 36229
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 36228 . 2 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
21simplbi 498 1 (𝐾 ∈ OL → 𝐾 ∈ Lat)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105  Latclat 17643  OPcops 36188  OLcol 36190
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-in 3940  df-ol 36194
This theorem is referenced by:  oldmm1  36233  oldmj1  36237  olj01  36241  olj02  36242  olm12  36244  latmassOLD  36245  latm12  36246  latm32  36247  latmrot  36248  latm4  36249  latmmdiN  36250  latmmdir  36251  olm01  36252  olm02  36253  omllat  36258  meetat  36312
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