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SUABCDF
SUabcdf
AOabcABC
ANBEPRQ+RABAP+RABCQ+EAabcABR  defn:anglelessthan
BEPRQ
RABCQ
EAabcABR
NCABR   lemma:equalanglesNC
ANRABCD+BEABF  defn:supplement
BEQRP  axiom:betweennesssymmetry
BEABF
BEFBA  axiom:betweennesssymmetry
RABAP
ORBEBPA|EQAP|BEBAP  lemma:ray1
cases BEFBP:BEBPA|EQAP|BEBAP
 case 1:BEBPA
  BEFBP axiom:innertransitivity
 qedcase
 case 2:EQAP
  BEFBP  cn:equalitysub
 qedcase
 case 3:BEBAP
  BEFBP lemma:3.7b
 qedcase
BEFBP cases
COFPQ  assumption
 COBAP  lemma:rayimpliescollinear
 COABF  defn:collinear
 NEAB  lemma:betweennotequal
 COABP  lemma:collinearorder
 COBFP  lemma:collinear4
 COFPB  lemma:collinearorder
 NEFP  lemma:betweennotequal
 COPQB lemma:collinear4
 COPBQ  lemma:collinearorder
 COPBA  lemma:collinearorder
 NEBP  lemma:betweennotequal
 NEPB  lemma:inequalitysymmetric
 COBQA lemma:collinear4
 COPRQ  defn:collinear
 COPQR  lemma:collinearorder
 COPQB lemma:collinearorder
 NEPQ  lemma:betweennotequal
 COQRB  lemma:collinear4
 COQBR  lemma:collinearorder
 COQBA lemma:collinearorder
 NEBQ  lemma:raystrict
 NEQB  lemma:inequalitysymmetric
 COBRA lemma:collinear4
 COABR lemma:collinearorder
 NCABR
NCFPQ reductio 
ANBEFMR+BEQMB  postulate:Pasch-inner
BEFMR
BEQMB
EQRR  cn:equalityreflexive
EQBR assumption
 COABR defn:collinear
NEBR reductio
RABRR  lemma:ray4
SUABRRF   defn:supplement
EAABRabc  lemma:equalanglessymmetric
EARBFdbf  lemma:supplements
NEBF  lemma:betweennotequal
EQFF  cn:equalityreflexive 
RABFF  lemma:ray4
EAdbfRBF  lemma:equalanglessymmetric
NCRBF  lemma:equalanglesNC
COFBQ assumption
 COQBF  lemma:collinearorder
 COQMB  defn:collinear
 COQBM  lemma:collinearorder
 NEQB   lemma:betweennotequal
 COBFM lemma:collinear4
 COFMR  defn:collinear
 COMFB  lemma:collinearorder
 COMFR  lemma:collinearorder
 NEFM   lemma:betweennotequal
 NEMF   lemma:inequalitysymmetric
 COFBR  lemma:collinear4
 CORBF  lemma:collinearorder
NCFBQ  reductio
RABFF
EAFBQFBQ lemma:equalanglesreflexive
BEBMQ  axiom:betweennesssymmetry
NEBM  lemma:betweennotequal
RABMQ  lemma:ray4
RABQM  lemma:ray5
EAFBQFBM  lemma:equalangleshelper
BERMF   axiom:betweennesssymmetry
RABRR
RABFF
AOFBQFBR   defn:anglelessthan
EAfbdFBR  lemma:equalanglesflip
EAFBRfbd  lemma:equalanglessymmetric
AOFBQfbd  lemma:angleorderrespectscongruence
RABCQ
RABCD
RABQD     lemma:ray3
EAFBQFBD  lemma:equalangleshelper
COFBD  assumption
 COBQD  lemma:rayimpliescollinear
 CODBQ  lemma:collinearorder
 CODBF  lemma:collinearorder
 NEBD   lemma:raystrict
 NEDB   lemma:inequalitysymmetric
 COBQF  lemma:collinear4
 COFBQ  lemma:collinearorder
 NCFBQ
NCFBD  reductio
EAFBDDBF  lemma:ABCequalsCBA
EAFBQDBF   lemma:equalanglestransitive
EADBFFBQ   lemma:equalanglessymmetric
AODBFfbd   lemma:angleorderrespectscongruence2
NCfbd    lemma:equalanglesNC
COdbf   assumption
 COfbd lemma:collinearorder
NCdbf reductio
EAdbffbd   lemma:ABCequalsCBA
AODBFdbf   lemma:angleorderrespectscongruence