Isotopically resolved fragments with $Z_{\sim }^{< }20$ have been studied with a high-resolution telescope in a test run for the FAZIA Collaboration. The fragments were produced by the collision of a $^{84}Kr$ beam at 35 MeV/nucleon with a neutron-rich ($^{124}Sn$) and a neutron-poor ($ ^{112}Sn $ ) target. The fragments, detected close to the grazing angle, are mainly emitted from the phase-space region of the projectile. The fragment isotopic content clearly depends on the neutron richness of the target and this is direct evidence of isospin diffusion between projectile and target. The observed enhanced neutron richness of light fragments emitted from the phase-space region close to the center of mass of the system can be interpreted as ...