Cut Edges and Spanning Trees

Prove: an edge e of a connected undirected simple graph G is a cut-edge if and only if it belongs to every spanning tree of G.

Pretty lost on this one. What's a way to connect cut-edges to tree, and how would one go about proving this?

• Hint: Prove that a cut edge can never be part of a cycle. – platty Aug 14 '17 at 14:17

An edge $e\in E(G)$ is a cut-edge $\Longleftrightarrow$ $G-e$ is disconnected.
A graph $G$ is disconnected $\Longleftrightarrow$ $G$ has no spanning trees.