Catalysis of the reactions: 1,5-anhydro-D-fructose = 2-hydroxy-2-(hydroxymethyl)-2H-pyran-3(6H)-one + H2O; (1a) 1,5-anhydro-D-fructose = 1,5-anhydro-4-deoxy-D-glycero-hex-3-en-2-ulose + H2O and (1b) 1,5-anhydro-4-deoxy-D-glycero-hex-3-en-2-ulose = 2-hydroxy-2-(hydroxymethyl)-2H-pyran-3(6H)-one.