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Theorem isolat 29947
Description: The predicate "is an ortholattice." (Contributed by NM, 18-Sep-2011.)
Assertion
Ref Expression
isolat  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )

Proof of Theorem isolat
StepHypRef Expression
1 df-ol 29913 . 2  |-  OL  =  ( Lat  i^i  OP )
21elin2 3523 1  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    e. wcel 1725   Latclat 14466   OPcops 29907   OLcol 29909
This theorem is referenced by:  ollat  29948  olop  29949  isolatiN  29951
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ol 29913
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