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PROBLEM TO BE SOLVED : To obtain a functional polymer having a specific structure in the molecule, high in ionic conductivity, excellent in processability, flexibility, mechanical strength and ionic transport number, thus useful as e.g. a solid polyelectrolyte. SOLUTION : This functional polymer has a structure expressed by the formula [X is CO-CFZ-SO2 or SO2 -CFZ-CO; Z is F or CF3 ; Y is H, ammonium, an alkali (alkaline earth) metal, transition metal or rare earth element; (n) is a positive integer of >=2]. The 2nd objective solid polyelectrolyte contains 10-100wt.% of this polymer, and the 3rd objective cell contains this solid polyelectrolyte connectedly sandwiched between electrodes.