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COABC
EEABab    
EEACac   
EEBCbc   
EECBBC   cn:equalityreverse
EECBbc   lemma:congruencetransitive
EEbccb   cn:equalityreverse
EECBcb   lemma:congruencetransitive
EEabba  cn:equalityreverse
EEABba  lemma:congruencetransitive
EEABBA  cn:equalityreverse
EEBAAB  lemma:congruencesymmetric
EEBAba  lemma:congruencetransitive
OREQAB|EQAC|EQBC|BEBAC|BEABC|BEACB  defn:collinear
cases COabc:EQAB|EQAC|EQBC|BEBAC|BEABC|BEACB 
 case 1: EQAB
  EEABab
  EEAAab cn:equalitysub
  EEabAA lemma:congruencesymmetric
  NEab assumption
   NEAA  axiom:nocollapse
   EQAA  cn:equalityreflexive
  EQab  reductio
  COabc defn:collinear
 qedcase
 case 2: EQAC
  EEACac
  EEAAac  cn:equalitysub
  EEacAA  lemma:congruencesymmetric
  NEac assumption
   NEAA axiom:nocollapse
   EQAA cn:equalityreflexive
  EQac  reductio
  COabc defn:collinear
 qedcase
 case 3: EQBC
  EEBCbc
  EEBBbc cn:equalitysub
  EEbcBB  lemma:congruencesymmetric
  NEbc assumption
   NEBB  axiom:nocollapse
   EQBB  cn:equalityreflexive
  EQbc  reductio
  COabc defn:collinear
 qedcase
 case 4: BEBAC
  BEbac  lemma:betweennesspreserved
  COabc  defn:collinear
 qedcase
 case 5: BEABC
  BEabc lemma:betweennesspreserved
  COabc  defn:collinear
 qedcase
 case 6: BEACB
  BEacb  lemma:betweennesspreserved
  COabc  defn:collinear
 qedcase
COabc cases

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