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

theorem Axiom5AFS:
  for S being satisfying_CongruenceSymmetry
              satisfying_CongruenceEquivalenceRelation
              satisfying_SAS
              TarskiGeometryStruct
  for a,b,c,d,a9,b9,c9,d9 being POINT of S st a,b,c,d AFS a9,b9,c9,d9 &
  a <> b holds c,d equiv c9,d9
  proof
    let S be satisfying_CongruenceSymmetry
             satisfying_CongruenceEquivalenceRelation
             satisfying_SAS
             TarskiGeometryStruct;
    let a,b,c,d,a9,b9,c9,d9 be POINT of S;
    assume
A1: a,b,c,d AFS a9,b9,c9,d9 & a <> b;
    S is satisfying_SST_A5;
    hence thesis by A1;
  end;
