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Theorem isolatiN 30088
Description: Properties that determine an ortholattice. (Contributed by NM, 18-Sep-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
isolati.1  |-  K  e. 
Lat
isolati.2  |-  K  e.  OP
Assertion
Ref Expression
isolatiN  |-  K  e.  OL

Proof of Theorem isolatiN
StepHypRef Expression
1 isolati.1 . 2  |-  K  e. 
Lat
2 isolati.2 . 2  |-  K  e.  OP
3 isolat 30084 . 2  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
41, 2, 3mpbir2an 888 1  |-  K  e.  OL
Colors of variables: wff set class
Syntax hints:    e. wcel 1726   Latclat 14479   OPcops 30044   OLcol 30046
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-in 3329  df-ol 30050
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