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COABC
EEABab
EEBCbc
EEADad
EECDcd
EEACac
NEAC
OREQAB|EQAC|EQBC|BEBAC|BEABC|BEACB   defn:collinear
OREQAB|EQBC|BEBAC|BEABC|BEACB
cases EEBDbd:EQAB|EQBC|BEBAC|BEABC|BEACB 
 case 1:EQAB
  EEBBab cn:equalitysub
  EEabBB lemma:congruencesymmetric
  NEab assumption
   NEBB  axiom:nocollapse
   EQBB  cn:equalityreflexive
  EQab   reductio
  EEBDad cn:equalitysub
  EEBDbd cn:equalitysub
 qedcase
 case 2:EQBC
  EEBBbc  cn:equalitysub
  EEbcBB  lemma:congruencesymmetric
  NEbc  assumption
   NEBB axiom:nocollapse
   EQBB cn:equalityreflexive
  EQbc  reductio
  EEBDcd  cn:equalitysub
  EEBDbd  cn:equalitysub
 qedcase
 case 3:BEBAC
  BECAB  axiom:betweennesssymmetry
  EECAca  lemma:congruenceflip
  EECBcb lemma:congruenceflip
  BEcab  lemma:betweennesspreserved
  EEDBdb axiom:5-line
  EEBDbd lemma:congruenceflip
 qedcase
 case 4:BEABC
  BEabc lemma:betweennesspreserved
  EEBDbd lemma:interior5
 qedcase
 case 5:BEACB
  EECBcb  lemma:congruenceflip
  BEacb lemma:betweennesspreserved
  EEDBdb axiom:5-line
  EEBDbd lemma:congruenceflip
 qedcase
EEBDbd cases

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