reserve X,Y,Z,X1,X2,Y1,Y2 for set, x,y,z,t,x1,x2 for object,
  f,g,h,f1,f2,g1,g2 for Function;

theorem
  proj1 X = {} iff proj2 X = {}
proof
  proj1 X = {} or proj2 X = {} implies
   not ex x,y being object st [x,y] in X by
XTUPLE_0:def 12,def 13;
  hence thesis by Th8;
end;
