theorem
  for F being Function of X,Y, y being Element of Y,
      z being Element of Z holds [:F,id Z:]"{[y,z]} = [:F"{y},{z}:]
proof
  let F be Function of X,Y, y be Element of Y, z be Element of Z;
  thus [:F,id Z:]"{[y,z]} = [:F,id Z:]"[:{y},{z}:] by ZFMISC_1:29
    .= [:F"{y},(id Z)"{z}:] by FUNCT_3:73
    .= [:F"{y},{z}:] by FUNCT_2:94;
end;
