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Theorem isolat 29379
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 29345 . 2  |-  OL  =  ( Lat  i^i  OP )
21elin2 3468 1  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    e. wcel 1717   Latclat 14395   OPcops 29339   OLcol 29341
This theorem is referenced by:  ollat  29380  olop  29381  isolatiN  29383
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2362
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2368  df-cleq 2374  df-clel 2377  df-nfc 2506  df-v 2895  df-in 3264  df-ol 29345
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