As per [Wikipeida](https://en.wikipedia.org/wiki/Spanning_tree#Fundamental_cycles), adding one more edge anywhere to any spanning tree would create a cycle. What's the proof?

I saw this property used in a proof about a [unique spanning tree for graphs with edges with unique weights](https://math.stackexchange.com/questions/352163/show-that-theres-a-minimum-spanning-tree-if-all-edges-have-different-costs). In a class a teacher once said you can use properties/theorems given earlier on in the textbook to where the question is being asked. When you're trying to prove something when can you use a property or theorem like this one?