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BEACB
NCABP
NECB   lemma:betweennotequal
NEBC  lemma:inequalitysymmetric
EQCP assumption
 NCABC  cn:equalitysub
 COACB  defn:collinear
 COABC  lemma:collinearorder
NECP  reductio
ANBEBCQ+EECQCP  lemma:extension
BEBCQ
EECQCP
EQPQ   assumption
 COBCQ  defn:collinear
 COBCP   cn:equalitysub
 COACB  defn:collinear
 COCBA  lemma:collinearorder
 COCBP  lemma:collinearorder
 COBAP  lemma:collinear4
 COABP  lemma:collinearorder
NEPQ reductio
ANBEPMQ+EEMPMQ  proposition:10
BEPMQ
EEMPMQ
COACB   defn:collinear
COCBA   lemma:collinearorder
NECB   lemma:betweennotequal
COCBQ   defn:collinear
COBAQ  lemma:collinear4
COABQ  lemma:collinearorder
NEAB   lemma:betweennotequal
NCABP
SSPPAB  lemma:samesidereflexive
NEQP lemma:inequalitysymmetric
BEQMP  axiom:betweennesssymmetry
RAQPM  lemma:ray4
COAQB  lemma:collinearorder
SSPMAB  lemma:sameside2
SSMPAB   lemma:samesidesymmetric
COABM   assumption
 COABQ
 COBMQ  lemma:collinear4
 COPMQ  defn:collinear
 COMQP  lemma:collinearorder
 COMQB lemma:collinearorder
 NEMQ  lemma:betweennotequal
 COQPB  lemma:collinear4
 COQBP   lemma:collinearorder
 COQBA   lemma:collinearorder
 NEBQ  lemma:betweennotequal
 NEQB  lemma:inequalitysymmetric
 COBPA  lemma:collinear4
 COABP  lemma:collinearorder
NCABM  reductio
PAMRABR  proposition:12
ANCOMRR+COABR+COABE+RRERM  defn:perpat
COABR
RRERM
RRMRE  lemma:8.2
COABC  lemma:collinearorder
RRACM  assumption
 NERC  assumption
  COBAC lemma:collinearorder
  COABR
  COBAR lemma:collinearorder
  NEBA  lemma:inequalitysymmetric
  COACR lemma:collinear4
  RRRCM  lemma:collinearright
  NORRMRC  lemma:8.7
  RRMRE
  RRERM  lemma:8.2
  COABE
  COABR
  COBCR  lemma:collinear4
  COBCE lemma:collinear4
  NECB  lemma:betweennotequal
  NEBC  lemma:inequalitysymmetric
  COCRE lemma:collinear4
  COERC  lemma:collinearorder
  NECR   lemma:inequalitysymmetric
  RRCRM lemma:collinearright
  RRMRC  lemma:8.2
 EQRC  reductio
 EQMC  assumption
  COABC
  COABM  cn:equalitysub
 NEMC  reductio
 EEQCPC  lemma:congruenceflip
 BEQMP  axiom:betweennesssymmetry
 EEQMPM  lemma:doublereverse
 RRQMC  defn:rightangle
 NECQ  lemma:betweennotequal
 NEQC  lemma:inequalitysymmetric
 RRERM  lemma:8.2
 NEQR   cn:equalitysub
 COABE
 COABQ
 COABR
 COBER  lemma:collinear4
 COBEQ  lemma:collinear4
 NEBE   assumption
  COERQ  lemma:collinear4
  RRQRM lemma:collinearright
  RRQCM  cn:equalitysub
  RRMCQ  lemma:8.2
  NORRQMC lemma:8.7
 EQBE  reductio
 COABR
 COAER  cn:equalitysub
 COABQ  lemma:collinearorder
 COAEQ  cn:equalitysub
 NEAE  cn:equalitysub
 COERQ lemma:collinear4
 RRQRM lemma:collinearright
 RRQCM  cn:equalitysub
 RRMCQ  lemma:8.2
 NORRQMC lemma:8.7 
NORRACM  reductio
ANNCABM+SSMPAB+NORRACM