The ideas used by Gibbs in defining the ideal gas mixture are brought to light in view of their fundamental significance and the fact that they have not received due attention in the literature. Specifically, the central role played by the well-known Gibbs-Duhem equation in this regard is explained. The concept of a fundamental equation and its importance in the definition of an ideal gas as well as an ideal gas mixture is elucidated. The manner in which these ideas enabled Gibbs to give a very general interpretation of Dalton's law is examined in detail.