In the proof of the Kruskal's algorithm given in class, we made this statement:
given two different trees $T$ and $T'$ on $n$ vertices, and given and edge $e \in E(T)\setminus E(T')$, consider the edge $e'$ such that $e' \in E(T')\setminus E(T)$ and $T\setminus \{e\} \cup \{e'\}$ is a tree on $n$ vertices ($E(T),E(T')$ denote the edge sets of $T$ and $T'$ respectively).
Now, intuitively I believe that such an $e'$ exists, but can I say that this always true?
Thank you