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EAABCabc
SUABCDF
SUabcdf
BEABF defn:supplement
RABCD defn:supplement
BEabf defn:supplement
RAbcd defn:supplement
EAABCabc
ANRABAU+RABCV+RAbau+RAbcv+EEBUbu+EEBVbv+EEUVuv+NCABC defn:equalangles
RABAU
RABCV
RAbau
RAbcv
EEBUbu
NEBU    lemma:raystrict
NEUB    lemma:inequalitysymmetric
NEbu   lemma:raystrict
NEub    lemma:inequalitysymmetric
ANBEUBW+EEBWUB  lemma:extension
BEUBW
BEabf
ANBEubw+EEbwUB  lemma:extension
BEubw
EEbwUB
EEBWUB
EEUBbw  lemma:congruencesymmetric
EEBWbw  lemma:congruencetransitive
EEUBub  lemma:congruenceflip
EEUVuv
EEBVbv
BEUBW
BEubw
EEVWvw axiom:5-line
BEUBW
BEABF
RABAU
ORBEBUA|EQAU|BEBAU lemma:ray1
cases BEABW:BEBUA|EQAU|BEBAU
 case 1:BEBUA
  BEAUB  axiom:betweennesssymmetry
  BEUBW  
  BEABW  lemma:3.7a
  qedcase
 case 2:EQAU
  BEABW  cn:equalitysub
  qedcase
 case 3:BEBAU
  BEUAB axiom:betweennesssymmetry
  BEUBW 
  BEABW lemma:3.6a
  qedcase
BEABW cases
RABFW  defn:ray
ORBEBWF|EQFW|BEBFW  lemma:ray1
cases BEUBF:BEBWF|EQFW|BEBFW
 case 1:BEBWF
  BEUBF  lemma:3.7b
  qedcase
 case 2:EQFW
  BEUBF  cn:equalitysub
  qedcase
 case 3:BEBFW
  BEUBF  axiom:innertransitivity
  qedcase
BEUBF  cases
ORBEbua|EQau|BEbau lemma:ray1
cases BEabw:BEbua|EQau|BEbau
 case 1:BEbua
  BEaub  axiom:betweennesssymmetry
  BEubw  
  BEabw  lemma:3.7a
  qedcase
 case 2:EQau
  BEabw  cn:equalitysub
  qedcase
 case 3:BEbau
  BEuab axiom:betweennesssymmetry
  BEubw 
  BEabw lemma:3.6a
  qedcase
BEabw cases
RAbfw defn:ray
CODBF  assumption
 COBCD  lemma:rayimpliescollinear
 CODBC  lemma:collinearorder
 NEBD   lemma:raystrict
 NEDB   lemma:inequalitysymmetric
 COBFC  lemma:collinear4
 COABF  defn:collinear
 COFBA  lemma:collinearorder
 COFBC  lemma:collinearorder
 NEBF   lemma:betweennotequal
 NEFB   lemma:inequalitysymmetric
 COBAC  lemma:collinear4
 COABC  lemma:collinearorder
 NCABC
NCDBF  reductio
RABDV   lemma:ray3
RABFW
RAbdv   lemma:ray3
RAbfw
EEBVbv
EEBWbw
EEVWvw
EADBFdbf defn:equalangles