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Theorem isolat 32210
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 32176 . 2  |-  OL  =  ( Lat  i^i  OP )
21elin2 3629 1  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 367    e. wcel 1842   Latclat 15997   OPcops 32170   OLcol 32172
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-v 3060  df-in 3420  df-ol 32176
This theorem is referenced by:  ollat  32211  olop  32212  isolatiN  32214
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