>if the proposition on which you built your proof is untrue then the proof is invalid as it is based on a false premise

Nope, you can have a false premise in a valid argument.
http://www.kcmetro.cc.mo.us/longview/ctac/soundness.htm
Once it is determined that an argument has a Valid form (it is a Deductive argument), the next step is to determine if all of the premises are indeed true.

And like I said, its a common technique to assume the opposite of what you want to prove and lead that to a contradiction:
http://www.friesian.com/valley/rules.htm
Assume the negation of the conclusion (P). The task then is to derive a
contradiction. If the contradiction involves the conclusion and its
negation, then the proof ends with an application of Conditionalization (C),
with the conclusion in the consequent, and Clavius (Th 16 or 17), to give
the conclusion, free of the added premise.