Child annuities shall be payable to each child of an employee annuitant who dies with no surviving spouse and whose spouse would have been eligible to receive a surviving spouse annuity, and each child of a deceased employee whose surviving spouse dies and whose spouse, immediately prior to death, was receiving or would have been eligible to receive, a surviving spouse annuity, or who left no surviving spouse, is eligible to receive a child annuity, provided:
40 ILCS 5/7-160