  A slight modification to one of Tarski's axioms of plane Euclidean geometry
is proposed. This modification allows another of the axioms to be omitted from
the set of axioms and proven as a theorem. This change to the system of axioms
simplifies the system as a whole, without sacrificing the useful modularity of
some of its axioms. The new system is shown to possess all of the known
independence properties of the system on which it was based; in addition,
another of the axioms is shown to be independent in the new system.
