Connectivity of cubic graphs and snarls

Prove that every cubic 3 edge-connected graph is 3-connected.

Let us define a snarl as a graph that can be obtained from \(K _ { 4 }\) by repeated applications of the operation of subdividing two edges and joining the two new vertices. Show that every snarl is 3-connected. (In fact it is true that every 3-connected cubic graph is a snarl.)