The fundamental metallicity relation (FMR) states that galaxies of the same stellar mass but larger star formation rate (SFR) tend to have smaller gas-phase metallicity (< {Z}g> ). It is thought to be fundamental because it naturally arises from the stochastic feeding of star formation from external metal-poor gas accretion, a process extremely elusive to observe but essential according the cosmological simulations of galaxy formation. In this Letter, we show how the FMR emerges from the local anti-correlation between SFR surface density and Z g recently observed to exist in disk galaxies. We analytically derive the global FMR from the local law, and then show that both relations agree quantitatively when considering the star-forming galaxies of the Mapping Nearby Galaxies at APO (MaNGA) survey. Thus, understanding the FMR becomes equivalent to understanding the origin of the anti-correlation between SFR and metallicity followed by the set of star-forming regions of any typical galaxy. The correspondence between local and global laws is not specific to the FMR, so that a number of local relations should exist that are associated with known global relations.