Full-field transmission X-ray microscopy is a unique non-destructive technique for three-dimensional imaging of specimens at the nanometer scale. Here, the use of zone-doubled Fresnel zone plates to achieve a spatial resolution better than 20 nm in the hard X-ray regime (8-10 keV) is reported. By obtaining a tomographic reconstruction of a Ni/YSZ solid-oxide fuel cell, the feasibility of performing three-dimensional imaging of scientifically relevant samples using such high-spatial-resolution Fresnel zone plates is demonstrated.