Histone demethylase required for brain development. Specifically demethylates dimethylated 'Lys-9' and 'Lys-27' (H3K9me2 and H3K27me2, respectively) of histone H3 and monomethylated histone H4 'Lys-20' residue (H4K20Me1), thereby playing a central role in histone code (By similarity). Binds 1 Fe(2+) ion per subunit. The PHD-type zinc finger mediates the binding to H3K4me3. Binding to H3K4me3 prevents its access to H3K9me2 (By similarity). Belongs to the JHDM1 histone demethylase family. JHDM1D subfamily.