reserve            S for satisfying_CongruenceSymmetry
                         satisfying_CongruenceEquivalenceRelation
                         TarskiGeometryStruct,
         a,b,c,d,e,f for POINT of S;

theorem Satz2p1bis:
  for S being satisfying_CongruenceEquivalenceRelation
              satisfying_SegmentConstruction
              TarskiGeometryStruct
  for a,b being POINT of S holds a,b equiv a,b
  proof
    let S be satisfying_CongruenceEquivalenceRelation
             satisfying_SegmentConstruction
             TarskiGeometryStruct;
    let a,b be POINT of S;
    ex c be POINT of S st between a,a,c & a,c equiv a,b by GTARSKI1:def 8;
    hence thesis by GTARSKI1:def 6;
  end;
