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Theorem isolatiN 33521
 Description: Properties that determine an ortholattice. (Contributed by NM, 18-Sep-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
isolati.1 𝐾 ∈ Lat
isolati.2 𝐾 ∈ OP
Assertion
Ref Expression
isolatiN 𝐾 ∈ OL

Proof of Theorem isolatiN
StepHypRef Expression
1 isolati.1 . 2 𝐾 ∈ Lat
2 isolati.2 . 2 𝐾 ∈ OP
3 isolat 33517 . 2 (𝐾 ∈ OL ↔ (𝐾 ∈ Lat ∧ 𝐾 ∈ OP))
41, 2, 3mpbir2an 957 1 𝐾 ∈ OL
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1977  Latclat 16868  OPcops 33477  OLcol 33479 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-in 3547  df-ol 33483 This theorem is referenced by: (None)
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