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Theorem isolat 37487
Description: The predicate "is an ortholattice." (Contributed by NM, 18-Sep-2011.)
Assertion
Ref Expression
isolat (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))

Proof of Theorem isolat
StepHypRef Expression
1 df-ol 37453 . 2 OL = (Lat ∩ OP)
21elin2 4144 1 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 396  wcel 2105  Latclat 18246  OPcops 37447  OLcol 37449
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3443  df-in 3905  df-ol 37453
This theorem is referenced by:  ollat  37488  olop  37489  isolatiN  37491
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