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Theorem isolat 36456
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 36422 . 2 OL = (Lat ∩ OP)
21elin2 4159 1 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399  wcel 2115  Latclat 17655  OPcops 36416  OLcol 36418
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-in 3926  df-ol 36422
This theorem is referenced by:  ollat  36457  olop  36458  isolatiN  36460
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