Histone demethylase that demethylates 'Lys-4' of histone H3, thereby playing a central role in histone code. Demethylates trimethylated H3 'Lys-4'. 3 2-oxoglutarate + N(6),N(6),N(6)-trimethyl-L-lysyl(4)-[histone H3] + 3 O2 = 3 CO2 + 3 formaldehyde + L-lysyl(4)-[histone H3] + 3 succinate Binds 1 Fe(2+) ion per subunit. The JmjC domain is required for enzymatic activity. Present with 290 molecules/cell in log phase SD medium. Belongs to the JARID1 histone demethylase family.