Phase contrast formed by inelastically scattered electrons in a crystal has been investigated using spatially resolved EELS, which enables simultaneous observation of lattice fringes formed by electrons of various energy losses. Lattice fringes produced by low-loss electrons overlap on an elastic TEM image like Fourier images. This means that the exit wave is preserved in low-loss scattering. Similar Fourier images occur for electrons suffering core-losses in the range 50-400 eV, which indicates delocalization and spatial coherence in those core-loss scattering events. The spatial coherence of inelastically scattered electrons is estimated from the focus dependence of energy-filtered lattice fringe contrast. Spatial coherence widths shorten with increasing energy-loss, and their energy-loss dependence is similar to diffraction errors derived from the characteristic angle for inelastic scattering.