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MIABC
MIPBQ
NEAP
ANBEABC+EEABBC  defn:midpoint
ANBEPBQ+EEPBBQ  defn:midpoint
BEABC
EEABBC
BEPBQ
EEPBBQ
cases EEAPCQ:COABP|NCABP
 case 1:COABP
  OREQAB|EQAP|EQBP|BEBAP|BEABP|BEAPB  defn:collinear
  cases EEAPCQ:EQAB|EQAP|EQBP|BEBAP|BEABP|BEAPB 
   case 1:EQAB
    NOEEAPCQ  assumption
     BEABC  defn:midpoint
     NEAB   lemma:betweennotequal
    EEAPCQ  reductio
   qedcase
   case 2:EQAP
    NOEEAPCQ assumption
	 NEAP
	EEAPCQ reductio
   qedcase
   case 3:EQBP
    NOEEAPCQ assumption
     NEPB  lemma:betweennotequal
     NEBP  lemma:inequalitysymmetric
    EEAPCQ reductio
   qedcase
   case 4:BEBAP
    EEPBBQ  
    EEABBC
    EEBCAB  lemma:congruencesymmetric
    EEBCBA   lemma:congruenceflip
    EEQBBP  lemma:doublereverse
    EEBQBP   lemma:congruenceflip
    EEBACB   lemma:doublereverse
    LTCBBP   defn:lessthan
    EEBPBQ   lemma:congruencesymmetric
    LTCBBQ   lemma:lessthancongruence
    EECBBC   cn:equalityreverse
    LTBCBQ   lemma:lessthancongruence2
    EEBQBQ   cn:congruencereflexive
    NEBQ    lemma:betweennotequal
    ANBEBHQ+EEBHBC  proposition:03
    BEBHQ
    EEBHBC
    RABQH    lemma:ray4
    BEPAB    axiom:betweennesssymmetry
    BEABC
    BEPBC    lemma:3.7a
    BEPBQ
    ANBEPBC+BEPBQ
    RABCQ    defn:ray
    RABQC    lemma:ray5
    EEBCBH   lemma:congruencesymmetric
    EQCH     lemma:layoffunique
    BEBCQ   cn:equalitysub 
    BEBAP    axiom:betweennesssymmetry
    EEBABC   lemma:congruencesymmetric
    EEBPBQ
    EEAPCQ  lemma:differenceofparts
   qedcase
   case 5: BEABP
	BEPBQ
    NOEEAPCQ   assumption
     BEBPC    assumption
      BECPB   axiom:betweennesssymmetry
      BECBQ   lemma:3.7a
      EEABCB  lemma:congruenceflip
      EEABCB
      EEBPBQ  lemma:congruenceflip
      EEAPCQ  cn:sumofparts
     NOBEBPC  reductio
     BEBCP    assumption
      BEABP   lemma:3.7b
      BEQBP   axiom:betweennesssymmetry
      BEQBC   axiom:innertransitivity
      BECBQ   axiom:betweennesssymmetry
      EEABCB  lemma:congruenceflip
      EEBPBQ  lemma:congruenceflip
      EEAPCQ  cn:sumofparts
     NOBEBCP  reductio
     EQPC     lemma:outerconnectivity
     EEABBC
     EEABBP   cn:equalitysub
     EEBPBQ   lemma:congruenceflip
     EEABBQ  lemma:congruencetransitive
     BECBA    axiom:betweennesssymmetry
     BEPBA    cn:equalitysub
     EEBQAB   lemma:congruencesymmetric
     EEBQBA   lemma:congruenceflip
     EQQA     lemma:extensionunique
     EEACCA    cn:equalityreverse
     EEAPCA    cn:equalitysub
     EEAPCQ    cn:equalitysub
    EEAPCQ  reductio
   qedcase
   case 6:BEAPB
    EEABBC  
    EEPBBQ
    EEBQPB  lemma:congruencesymmetric
    EEBQBP   lemma:congruenceflip
    EECBBA  lemma:doublereverse
    EEBCBA   lemma:congruenceflip
    BEBPA    axiom:betweennesssymmetry
    EEBPQB   lemma:doublereverse
    LTQBBA   defn:lessthan
    EEBABC   lemma:congruencesymmetric
    LTQBBC   lemma:lessthancongruence
    EEQBBQ   cn:equalityreverse
    LTBQBC   lemma:lessthancongruence2
    EEBCBC   cn:congruencereflexive
    NEBC    lemma:betweennotequal
    ANBEBHC+EEBHBQ  proposition:03
    BEBHC
    EEBHBQ
    BEABC
    BEPBC    lemma:3.6a
    BEPBQ
    ANBEPBC+BEPBQ
    RABCQ    defn:ray
    RABCH    lemma:ray4
    EEBQBH   lemma:congruencesymmetric
    EQQH     lemma:layoffunique
    BEBQC   cn:equalitysub
    BEBPA    axiom:betweennesssymmetry
    EEBPBQ   lemma:congruencesymmetric
    EEBABC
    EEPAQC  lemma:differenceofparts
    EEAPCQ  lemma:congruenceflip
   qedcase
  EEAPCQ cases 
 qedcase
 case 2:NCABP
  EAABPQBC   proposition:15
  NCQBC  lemma:equalanglesNC
  EAQBCCBQ   lemma:ABCequalsCBA
  EAABPCBQ   lemma:equalanglestransitive
  EEBABC    lemma:congruenceflip
  EEBPBQ    lemma:congruenceflip
  EEAPCQ    proposition:04
 qedcase
EEAPCQ  cases