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

theorem Satz2p2bis:
  for S being satisfying_CongruenceEquivalenceRelation
              satisfying_SegmentConstruction
              TarskiGeometryStruct
  for a,b,c,d being POINT of S st a,b equiv c,d holds c,d equiv a,b
  proof
    let S be satisfying_CongruenceEquivalenceRelation
             satisfying_SegmentConstruction
             TarskiGeometryStruct;
    let a,b,c,d be POINT of S;
    assume
A1: a,b equiv c,d;
    a,b equiv a,b by Satz2p1bis;
    hence thesis by A1,GTARSKI1:def 6;
  end;
