Need to prove that a transportation problem is never degenerate

Question

This is the question:

where a_i is the supply from source_i and b_j is the demand at destination_j.
I can kind of see why this would happen: say, when we are comparing a₁ to b₁ + 1/n, regardless of which of these two numbers is smaller (and they can't be equal since one of them is an integer and the other is not), we will end up with at least two basic variables. This will go on until the rightmost and the bottom-most comparison is being made, which is when we would only get one basic variable. So in all, we will always have 1 (n times) + 1 (m times) - 1 = n + m - 1 basic variables which means that the solution would never be degenerate.
However, this certainly doesn't feel the right way to go around proving this. I have tried Googling and looked up in the Google Books results that popped up - but couldn't find a solution. Hence decided to ask here. Thanks in advance.