Problem #PRU-5252

Problem

In a graph $G$, we call a matching any choice of edges in $G$ in such a way that all vertices have only one edge among chosen connected to them. A perfect matching is a matching which is arranged on all vertices of the graph.
Let $G$ be a graph with $2n$ vertices and all the vertices have degree at least $n$ (the number of edges exiting the vertex). Prove that one can choose a perfect matching in $G$.