# Transforming spanning trees through a sequence of intermediate trees

the problem is as follows: Let $G$ be a connected graph, and let $T_1$ and $T_2$ be two of its spanning trees. Prove that $T_1$ can be transformed into $T_2$ through a sequence of intermediate trees, each arising from the previous one and adding another.

I am confused whether this is a regular spanning tree problem which can be solved with Kruskal's greedy algorithm or if it is a question related to Huffman's algorithm. That is what I would like to know first, but the process of transforming one spanning tree into another through a sequence of intermediate trees is something that I am able to find a good example of online.

All you need to do is prove this lemma: given two distinct spanning trees $T_1$ and $T_2$ in graph $G$, it is possible to remove an edge from $T_1$ and add to it an edge from $T_2$ such that the resulting subgraph of $G$ is again a spanning tree.