reserve AS for AffinSpace;
reserve A,K,M,X,Y,Z,X9,Y9 for Subset of AS;
reserve zz for Element of AS;
reserve x,y for set;

theorem Th2:
  AS is AffinPlane & X is being_plane implies X = the carrier of AS
proof
  assume that
A1: AS is AffinPlane and
A2: X is being_plane;
  the carrier of AS c= the carrier of AS;
  then reconsider Z=the carrier of AS as Subset of AS;
  Z is being_plane by A1,Th1;
  hence thesis by A2,AFF_4:33;
end;
