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EEABab
EEACac
BEABC
BEabc
cases EEBCbc:EQBA|NEBA
 case 1: EQBA    
  EEAAab  cn:equalitysub
  EEabAA  lemma:congruencesymmetric
  NEab   assumption
   NEAA  axiom:nocollapse
   EQAA  cn:equalityreflexive
  EQab    reductio
  EEACAC   cn:congruencereflexive
  EEBCAC   cn:equalitysub
  EEBCac   lemma:congruencetransitive
  EEbcbc   cn:congruencereflexive
  EEbcac   cn:equalitysub
  EEacbc   lemma:congruencesymmetric
  EEBCbc   lemma:congruencetransitive
 qedcase
 case 2: NEBA  
  EQCA    assumption
  BEABA   cn:equalitysub  
  NOBEABA   axiom:betweennessidentity
  NECA    reductio
  NEAC    lemma:inequalitysymmetric
  ANBECAE+EEAEAC   lemma:localextension
  EEACac
  BECAE
  NEAC    lemma:inequalitysymmetric
  NEac    axiom:nocollapse
  NEca    lemma:inequalitysymmetric
  ANBEcae+EEaeac   lemma:localextension
  BEcae
  EEAEAC
  EEaeac
  EEEAAE   cn:equalityreverse
  EEEAAC   lemma:congruencetransitive
  EEACac
  EEEAac   lemma:congruencetransitive
  EEeaae   cn:equalityreverse
  EEeaac   lemma:congruencetransitive
  EEacea   lemma:congruencesymmetric
  EEEAac   lemma:congruencetransitive
  EEEAea   lemma:congruencetransitive
  BEEAC    axiom:betweennesssymmetry
  BEeac    axiom:betweennesssymmetry
  EEECec   cn:sumofparts
  EEECec
  EEEAea
  EEABab
  BEEAC
  BEABC
  BEEAB   axiom:innertransitivity
  BEeab   axiom:innertransitivity
  EECBcb  axiom:5-line
  EEbcBC  lemma:doublereverse
  EEBCbc  lemma:congruencesymmetric
 qedcase
EEBCbc  cases

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