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 Th52:
  not Collinear a,b,c implies for E1,E2 being Subset of S st E1 is_plane &
  a in E1 & b in E1 & c in E1 & E2 is_plane & a in E2 & b in E2 & c in E2
  holds E1 = E2
  proof
    assume
A1: not Collinear a,b,c;
    let E1,E2 being Subset of S such that
A2: E1 is_plane & a in E1 & b in E1 & c in E1 and
A3: E2 is_plane & a in E2 & b in E2 & c in E2;
    thus E1 = Plane(a,b,c) by A1,A2,Th47
           .= E2 by A1,A3,Th47;
  end;
