Should a transferred member who was a member of the city system under Article V of this chapter prior to his or her transfer die before retirement from causes other than injuries received in or illnesses incurred in the performance of duty and while a member of the county system or after retirement under the county system, the city system shall be liable for the applicable death benefit provided in Sections 2.124.770, 2.124.780, 2.124.790, 2.124.800 and 2.124.810 of Article V of this chapter; provided, that if no allowance is payable on account of such death before retirement, the amount payable by the city system shall not be less than the member's accumulated contributions; and provided further that any allowance payable under such sections shall be calculated on the assumption that the service rendered by said member to the county was rendered instead to such city, at the same rate of compensation paid by the county for such service and that any allowance so calculated upon death shall be reduced by an amount which is the actuarial equivalent of the death benefit payable by the county system and further reduced by the amount of any allowance payable by the county system because of the automatic continuance of all or part of such member's allowance under the county system. (Prior code § 34.07.706)