Graph theory

Hey guys, I could use some advice. I'm sitting a Maths exam tomorrow and one of the modules is on graph theory.
I've been doing revision problems from past papers, but they don't release the solutions. Most of it is fine, but what I require help with is this:

For a connected simple graph G, prove that for any two edges of G there is a spanning tree that includes both edges.

I've had a go at it but my attempt at a proof didn't even convince myself. I would really appreciate any help to find a reasonably elegant and decisive proof.

I might be wrong, but I think it should be something like this:

- Every simple connected graph can be turned into a spanning tree by removing it's cycles.
- Every cycle (in a undirected graph) must have at least 3 edges
- To remove a cycle, only one edge needs to be removed.
- Therefore, if for every cycle ypu can keep at least to edges intact.