Consider an undirected, simple graph $G= (V,E)$ with edge weights $w_e\geq 0$,$e \in E$. Then any two minimum spanning trees$T_1$ and $T_2$ for $G$ must have a nonempty intersection, that is $T_1 \cap T_2 \neq \varnothing$
I know that even if the edge weights are not all identical you can have two disjoint minimum spanning trees. But how do I prove this mathematically?