reserve A for non empty set,
  a,b,x,y,z,t for Element of A,
  f,g,h for Permutation of A;

theorem Th1:
  ex x st f.x=y
proof
  rng f = A by FUNCT_2:def 3;
  then ex x being object st x in dom f & f.x = y by FUNCT_1:def 3;
  hence thesis;
end;
