reserve S for non empty satisfying_CongruenceIdentity
              satisfying_SegmentConstruction
              satisfying_BetweennessIdentity
              satisfying_Pasch
              TarskiGeometryStruct;
reserve a,b for POINT of S;
reserve A for Subset of S;
reserve S for non empty satisfying_Tarski-model
              TarskiGeometryStruct;
reserve a,b,c,m,r,s for POINT of S;
reserve A for Subset of S;
reserve S         for non empty satisfying_Lower_Dimension_Axiom
                                satisfying_Tarski-model
                                TarskiGeometryStruct,
        a,b,c,d,m,p,q,r,s,x for POINT of S,
        A,A9,E              for Subset of S;

theorem Th43:
  A,A9 Is p implies A c= Plane(A,A9) & A9 c= Plane(A,A9) &
  Plane(A,A9) = Plane(A9,A)
  proof
    assume A,A9 Is p;
    then A c= Plane(A9,A) & A9 c= Plane(A,A9) &
    Plane(A,A9) = Plane(A9,A) by Th39,Th40,Th42;
    hence thesis;
  end;
