reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;

theorem
  {z} c= {x,y} implies z = x or z = y
proof
A1: z in {z} by TARSKI:def 1;
  assume {z} c= {x,y};
  then z in {x,y} by A1;
  hence thesis by TARSKI:def 2;
end;
