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Theorem isolat 35368
 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 35334 . 2 OL = (Lat ∩ OP)
21elin2 4024 1 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 198   ∧ wa 386   ∈ wcel 2107  Latclat 17431  OPcops 35328  OLcol 35330 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-ext 2754 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-v 3400  df-in 3799  df-ol 35334 This theorem is referenced by:  ollat  35369  olop  35370  isolatiN  35372
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