reserve            S for satisfying_CongruenceSymmetry
                         satisfying_CongruenceEquivalenceRelation
                         TarskiGeometryStruct,
         a,b,c,d,e,f for POINT of S;
reserve S for satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_SAS
              TarskiGeometryStruct,
        q,a,b,c,a9,b9,c9,x1,x2 for POINT of S;
reserve S for satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct,
        a,b,c,d for POINT of S;
reserve       S for satisfying_Tarski-model TarskiGeometryStruct,
        a,b,c,d for POINT of S;
reserve         S for satisfying_CongruenceIdentity
                      satisfying_SegmentConstruction
                      satisfying_BetweennessIdentity
                      satisfying_Pasch
                      TarskiGeometryStruct,
        a,b,c,d,e for POINT of S;
reserve       S for satisfying_Tarski-model
                    TarskiGeometryStruct,
      a,b,c,d,p for POINT of S;

theorem Satz3p14:
  for S being satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_Lower_Dimension_Axiom
              TarskiGeometryStruct holds
  for a,b being POINT of S ex c being POINT of S st between a,b,c & b <> c
  proof
    let S be satisfying_CongruenceSymmetry
             satisfying_CongruenceEquivalenceRelation
             satisfying_CongruenceIdentity
             satisfying_SegmentConstruction
             satisfying_Lower_Dimension_Axiom
             TarskiGeometryStruct;
    let a,b be POINT of S;
    consider u,v,w be POINT of S such that
A1: not between u,v,w & not between v,w,u & not between w,u,v & u <> v &
      v <> w & w <> u by Satz3p13;
    consider x be POINT of S such that
A2: between a,b,x & b,x equiv u,v by GTARSKI1:def 8;
    b <> x by A1,A2,Satz2p2,GTARSKI1:def 7;
    hence thesis by A2;
  end;
