Originally Posted by **albi**

I'm quite sure about that. The only way of showing that q is conclusion from p is to construct a proof based on some axioms. No matter if p is true or not if we show that p implies q (assuming p true) and than that ~p implies q (assuming the other possibility) there is no other way than to conclude that q is true (cause there is no more logical value p can have, "tertium non datur"). Proving the implications we use axioms so q is conclusion from axioms indeed.

If you have found some mistake please tell me about it.

To PerfectHacker: I haven't ever seen proof like this. I will try to think out if I have some time.

Sorry for 'prooving' in the previous post. My English isn't very good.

Goodnight