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Theorem ollat 34019
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 34018 . 2 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
21simplbi 476 1 (𝐾 ∈ OL → 𝐾 ∈ Lat)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1987  Latclat 16985  OPcops 33978  OLcol 33980
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3192  df-in 3567  df-ol 33984
This theorem is referenced by:  oldmm1  34023  oldmj1  34027  olj01  34031  olj02  34032  olm12  34034  latmassOLD  34035  latm12  34036  latm32  34037  latmrot  34038  latm4  34039  latmmdiN  34040  latmmdir  34041  olm01  34042  olm02  34043  omllat  34048  meetat  34102
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