This invention discloses and claims methods for inhibiting bacterial β-lactamases and treating bacterial infections by inhibiting bacterial β-lactamases in man or an animal comprising administering a therapeutically effective amount to said man or said animal of a compound, or pharmaceutically acceptable salt thereof, of formula (I) either alone or in combination with a β-lactamine antibiotic wherein said combination can be administered separately, together or spaced out over time. Pharmaceutical compositions comprising a compound of formula (I), or a combination of a compound of formula (I) and a therapeutically effective amount of a β-lactamine antibiotic, and a pharmaceutically acceptable carrier are also disclosed and claimed.