Whenever any banking institution shall have been closed as aforesaid, and the Federal Deposit Insurance Corporation shall pay or make available for payment the insured deposit liabilities of such closed institution, the corporation, whether or not it shall have become receiver or liquidator of such closed banking institution as herein provided, shall be subrogated to all rights against such closed banking institution of the owners of such deposits in the same manner and to the same extent as subrogation of the corporation is provided for in subsection (1) of section 12B of the Federal Reserve Act, as amended (being section 8, of the Banking Act of 1933) in the case of the closing of a national bank; Provided, that the rights of depositors and other creditors of such closed institution shall be determined in accordance with the applicable provisions of the laws of this state.