Quick Question on Minimal Spanning Trees

Question

If some edge from the spanning tree T0 is contained in some minimal spanning tree T *, does this mean that T0 is also a minimal spanning tree?

Right now, I'm trying to draw some graphs on paper to prove that this is not the case. Please correct me if this happens, or help me find an example if this is not the case.

Thanks in advance.

Answer 1

Triangle with weights of ribs 2,2,1.

EDIT:

3 (1 + 2), 3 (2 + 1) 4 (2 + 2). 4 3 .