Stability implications of Bendixson's criterion

A planar differential equation x = P(x,y), y= Q(x,y) is considered, where P and Q are real-valued continuously differentiable functions on R(super2). An accessible proof for 2-dimensional systems is presented, using only elementary techniques, proving that the omega limit set of a solution to the planar system, that satisfies the Bendixson criterion is a single equilibrium or is empty.