Users' Mathboxes Mathbox for Norm Megill < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  isolat Structured version   Unicode version

Theorem isolat 33220
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 33186 . 2  |-  OL  =  ( Lat  i^i  OP )
21elin2 3652 1  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    e. wcel 1758   Latclat 15338   OPcops 33180   OLcol 33182
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3080  df-in 3446  df-ol 33186
This theorem is referenced by:  ollat  33221  olop  33222  isolatiN  33224
  Copyright terms: Public domain W3C validator