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Theorem olop 34020
Description: An ortholattice is an orthoposet. (Contributed by NM, 18-Sep-2011.)
Assertion
Ref Expression
olop (𝐾 ∈ OL → 𝐾 ∈ OP)

Proof of Theorem olop
StepHypRef Expression
1 isolat 34018 . 2 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
21simprbi 480 1 (𝐾 ∈ OL → 𝐾 ∈ OP)
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:  olposN  34021  oldmm1  34023  oldmm2  34024  oldmm3N  34025  oldmm4  34026  oldmj1  34027  oldmj2  34028  oldmj3  34029  oldmj4  34030  olj01  34031  olj02  34032  olm11  34033  olm12  34034  latmassOLD  34035  olm01  34042  olm02  34043  omlop  34047  meetat  34102  hlop  34168  polatN  34736
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