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Theorem isolat 35287
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 35253 . 2 OL = (Lat ∩ OP)
21elin2 4028 1 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
Colors of variables: wff setvar class
Syntax hints:  wb 198  wa 386  wcel 2166  Latclat 17398  OPcops 35247  OLcol 35249
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-ext 2803
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-v 3416  df-in 3805  df-ol 35253
This theorem is referenced by:  ollat  35288  olop  35289  isolatiN  35291
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