Fast question about minimum spanning trees 
If any edge from a given spanning tree T0 is contained by a minimum spanning tree T*, does this imply that T0 is also a minimum spanning tree ?

Right now, I'm trying to draw on paper some graphs to prove that it doesn't. Please correct me if it does, or help me find an example if it doesn't.

Thanks in advance.
Fast question about minimum spanning trees 
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If any edge from a given spanning tree T0 is contained by a minimum spanning tree T*, does this imply that T0 is also a minimum spanning tree ?

Right now, I'm trying to draw on paper some graphs to prove that it doesn't. Please correct me if it does, or help me find an example if it doesn't.

Thanks in advance.