The following statement is investigated: if electrons realize an equilibrium between ionization and recombination in a two-temperature radiationless plasma, then the Saha equation can be obtained by replacing the thermodynamic temperature by the electron temperature. It is found that the statement is in general rather academic, but becomes realistic if it is confined to the higher excited states. These states are in so-called partial local Saha equilibrium (pLSE). The elementary mass action law (EMAL) is used to derive the Saha equation for pLSE conditions and the method is compared to a derivation based on the maximum entropy principle (MEP). This comparison reveals why the complicated two-temperature Saha variants as found in literature are incorrect and why the EMAL is much more suitable than the MEP to treat partial equilibria. Experimental evidence proves once more that the complicated two-temperature Saha equations are incorrect and that the statement is justified as long as we confine ourselves to the pLSE part of the system.