No other provision of law which provides wholly or partly at the expense of the city for pensions or retirement benefits for employees in the city-service, shall apply to such employees who become members or beneficiaries of the retirement system provided for by this chapter, their widows or their other dependents. This chapter shall not apply to any person who is, or may be, entitled to share in the police pension fund, or in the fire department relief fund, or in the teachers' retirement system, or in the Hunter College retirement system, or in the department of street cleaning relief and pension fund (except as provided in section 13-614 of this title), or in the board of education retirement system, by reason of service of such person as an employee under provisions of law applicable to such funds. Notwithstanding the foregoing provisions of this section, nothing therein contained shall prevent a member of this retirement system whose membership is authorized by subdivision three of section 13-104 of this chapter, upon his or her retirement from this retirement system, or his or her widow, dependents, or beneficiaries, upon his or her death, from receiving benefits from this retirement system, as well as benefits to which they may be entitled from any other retirement system or pension fund maintained by the city.