This work studies the relation between gas-phase oxygen abundance and stellar-togas fraction in nearby galaxies. We first derive the theoretical prediction, and argue that this relation is fundamental, in the sense that it must be verified regardless of the details of the gas accretion and star formation histories. Moreover, it should hold on 'local' scales, i.e. in regions of the order of 1 kpc. These predictions are then compared with a set of spectroscopic observations, including both integrated and resolved data. Although the results depend somewhat on the adopted metallicity calibration, observed galaxies are consistent with the predicted relation, imposing tight constraints on the mass-loading factor of (enriched) galactic winds. The proposed parametrization of the star fraction-metallicity relation is able to describe the observed dependence of the oxygen abundance on gas mass at fixed stellar mass. However, the 'local' mass-metallicity relation also depends on the relation between stellar and gas surface densities.