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Theorem isolat 28775
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 28741 . 2  |-  OL  =  ( Lat  i^i  OP )
21elin2 3359 1  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    e. wcel 1684   Latclat 14151   OPcops 28735   OLcol 28737
This theorem is referenced by:  ollat  28776  olop  28777  isolatiN  28779
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-ol 28741
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