theorem Lm4p14p1:
  for S being satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              TarskiGeometryStruct
  for a,b,c,a9,b9,c9 being POINT of S st b,a,c cong b9,a9,c9 holds
  a,b,c cong a9,b9,c9
  proof
    let S be satisfying_CongruenceSymmetry
             satisfying_CongruenceEquivalenceRelation
             TarskiGeometryStruct;
    let a,b,c,a9,b9,c9 be POINT of S;
    assume
A1: b,a,c cong b9,a9,c9;
    then a,b equiv b9,a9 by Satz2p4;
    hence a,b,c cong a9,b9,c9 by A1,Satz2p5;
  end;
