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PRACBD
NOCRABCD
PRBDAC  lemma:parallelsymmetric
TPBDAC  lemma:paralleldef2B
SSACBD  defn:tarski_parallel
NCACB  lemma:parallelNC
NEAB   lemma:NCdistinct
ANBEABE+EEBEAB  lemma:extension
BEABE
EQBB  cn:equalityreflexive
COBDB  defn:collinear
NCABD  lemma:parallelNC
NCBDA  lemma:NCorder
SSCABD  lemma:samesidesymmetric
OSABDE defn:oppositeside
OSCBDE  lemma:planeseparation
ANBECFE+COBDF+NCBDC  defn:oppositeside
BECFE
COBDF
NCBDC
NEBD  lemma:NCdistinct
NCABD  lemma:parallelNC
NEAD  lemma:NCdistinct
NCACD  lemma:parallelNC
NEAC  lemma:NCdistinct
NECD  lemma:NCdistinct
NECA  lemma:inequalitysymmetric
NCACB  lemma:parallelNC
NECB  lemma:NCdistinct
NEBC  lemma:inequalitysymmetric
OREQBD|EQBF|EQDF|BEDBF|BEBDF|BEBFD  defn:collinear
cases CRADBC:EQBD|EQBF|EQDF|BEDBF|BEBDF|BEBFD
 case 1:EQBD
  NOCRADBC assumption
   NEBD
  CRADBC reductio
 qedcase
 case 2:EQBF
  NOCRADBC assumption
   COCFE  defn:collinear
   COEFC  lemma:collinearorder
   NEBE  lemma:betweennotequal
   COABE  defn:collinear
   COEBA  lemma:collinearorder
   COEFC  lemma:collinearorder
   COEBC  cn:equalitysub
   NEEB lemma:inequalitysymmetric
   COBAC  lemma:collinear4
   COACB  lemma:collinearorder
   NCACB  lemma:parallelNC
  CRADBC reductio
 qedcase
 case 3:EQDF
  NCACB  lemma:parallelNC
  NCACF  cn:equalitysub
  NCCFA  lemma:NCorder
  COCFE   defn:collinear
  EQCC    cn:equalityreflexive
  COCFC   defn:collinear
  NECE  lemma:betweennotequal
  NCCEA   lemma:NChelper
  NCAEC   lemma:NCorder
  ANBEAMF+BECMB postulate:Pasch-inner
  BEAMF
  BECMB
  BEAMD  cn:equalitysub
  BEBMC  axiom:betweennesssymmetry
  ANNEAD+NEBC+BEAMD+BEBMC
  CRADBC  defn:cross
 qedcase
 case 4:BEDBF
  NOCRADBC assumption
   BECFE
   NCDBC  lemma:NCorder
   EQDD  cn:equalityreflexive
   CODBD  defn:collinear
   CODBF  lemma:collinearorder
   NEDF  lemma:betweennotequal
   NCDFC  lemma:NChelper
   NCCFD  lemma:NCorder
   COCFE  defn:collinear
   EQCC   cn:equalityreflexive
   COCFC  defn:collinear
   NECE   lemma:betweennotequal
   NCCED lemma:NChelper
   NCECD  lemma:NCorder
   BEEFC  axiom:betweennesssymmetry
   ANBEDMC+BEEBM  postulate:Pasch-outer
   BEDMC
   BEEBM
   BECMD  axiom:betweennesssymmetry
   BEMBE  axiom:betweennesssymmetry
   COABE  defn:collinear
   COEBM  defn:collinear
   COEBA  lemma:collinearorder
   NEBE   lemma:betweennotequal
   NEEB   lemma:inequalitysymmetric
   COBMA  lemma:collinear4
   COABM  lemma:collinearorder
   PRCABD  lemma:parallelflip
   NOMECABD  defn:parallel
   EQAA  cn:equalityreflexive
   COCAA   defn:collinear
   EQBB  cn:equalityreflexive
   COBBD   defn:collinear
   NECA 
   NEBD
   COABM 
   BEAMB   lemma:collinearbetween
   ANNEAB+NECD+BEAMB+BECMD
   CRABCD  defn:cross
   NOCRABCD
  CRADBC reductio
 qedcase
 case 5:BEBDF
  BECFE
  NCACB  lemma:parallelNC
  EQAA  cn:equalityreflexive
  COABA defn:collinear
  COABE  defn:collinear
  NEAE  lemma:betweennotequal
  NCABC  lemma:NCorder
  NCAEC  lemma:NChelper
  COAEB lemma:collinearorder
  EQEE  cn:equalityreflexive
  COAEE  defn:collinear
  NEBE  lemma:betweennotequal
  NCBEC  lemma:NChelper
  NCCEB  lemma:NCorder
  ANBEBJE+BECDJ  postulate:Pasch-outer
  BEBJE
  BEABE
  BEAJE  lemma:3.5b
  NCACB  lemma:parallelNC
  NCABC  lemma:NCorder
  COAJE  defn:collinear
  COEAB  lemma:collinearorder
  COEAJ  lemma:collinearorder
  NEAE  lemma:betweennotequal
  NEEA   lemma:inequalitysymmetric
  COABJ  lemma:collinear4
  NEAJ lemma:betweennotequal
  NCAJC  lemma:NChelper 
  BEBJE
  BEABE
  BEABJ  axiom:innertransitivity
  BECDJ
  ANBEAMD+BECMB  postulate:Pasch-inner
  BEAMD
  BECMB  
  BEBMC  axiom:betweennesssymmetry
  ANBEAMD+BEBMC
  CRADBC  defn:cross
 qedcase
 case 6:BEBFD
  BEDFB  axiom:betweennesssymmetry
  BEEBA  axiom:betweennesssymmetry
  NCABD  lemma:parallelNC
  COABE  defn:collinear
  EQAA  cn:equalityreflexive
  COABA  defn:collinear
  NEAE  lemma:betweennotequal
  NCAED lemma:NChelper
  NCEAD  lemma:NCorder
  ANBEDQA+BEEFQ  postulate:Pasch-outer
  BEDQA
  BEEFQ
  BEEFC  axiom:betweennesssymmetry
  COEFQ  defn:collinear
  COEFC  defn:collinear
  NEFE  lemma:betweennotequal
  NEEF  lemma:inequalitysymmetric
  COFQC  lemma:collinear4
  COFCQ  lemma:collinearorder
  BEAQD  axiom:betweennesssymmetry
  PRACBD
  COBFD  defn:collinear
  COBDF  lemma:collinearorder
  NEFD  lemma:betweennotequal
  PRACFD  lemma:collinearparallel
  NOMEACFD  defn:parallel
  EQCC  cn:equalityreflexive
  EQFF  cn:equalityreflexive
  COACC  defn:collinear
  COFFD  defn:collinear
  NEAC
  NEFD 
  COCFQ  lemma:collinearorder
  BECQF  lemma:collinearbetween
  NCACB  lemma:parallelNC
  NCABC  lemma:NCorder
  COABA  defn:collinear
  COABE defn:collinear
  NEAE  lemma:betweennotequal
  NCAEC  lemma:NChelper
  BEABE
  BECQE  lemma:3.6b
  ANBEAMQ+BECMB  postulate:Pasch-inner
  BEAMQ
  BECMB
  BEAMD  lemma:3.6b
  BEBMC  axiom:betweennesssymmetry
  CRADBC  defn:cross
 qedcase
CRADBC cases