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Theorem isolat 34014
 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 33980 . 2 OL = (Lat ∩ OP)
21elin2 3784 1 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196   ∧ wa 384   ∈ wcel 1987  Latclat 16977  OPcops 33974  OLcol 33976 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 3191  df-in 3566  df-ol 33980 This theorem is referenced by:  ollat  34015  olop  34016  isolatiN  34018
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