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Theorem isolatiN 29699
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 29695 . 2  |-  ( K  e.  OL  <->  ( K  e.  Lat  /\  K  e.  OP ) )
41, 2, 3mpbir2an 887 1  |-  K  e.  OL
Colors of variables: wff set class
Syntax hints:    e. wcel 1721   Latclat 14429   OPcops 29655   OLcol 29657
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 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-v 2918  df-in 3287  df-ol 29661
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