In a bipartite graph $(X,Y)$ where $|x|=|y|=n$ and $\delta(G) >= n/2$ there is a perfect matching

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Suppose $G$ is a bipartite graph with bipartition $(X,Y)$ such that $|X|=|Y|=n$ and $\delta(G) >= n/2$. Prove that Hall's condition for this graph is true, meaning there is a perfect matching in this graph.