# Proving that each graph contains a spanning tree?

as a part of Discrete Mathematics course we are taking an introduction to graph theory. We got this question for homework:

Let $G=(V,E)$ a connected graph. Prove that there exist a sub-graph $H$ of $G$ such that $H$ is a tree and include all of $G$'s vertices.

So, I immediately thought of the process of removing all the edges of $G$ such that their removal will not increase the number of connected components, thus insuring that we have a connected cycle-free graph, which is a tree.

My question: is describing this process makes a valid proof? This course is only introductory so we're not very formal, but I still want to make sure that the possibility of this process on any connected graph proves the existence of a tree.

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