Do I have to discharge an antecedent that I assume? For example, if I have the premise:
$P \rightarrow (Q \rightarrow R)$
Can I assume P to get:
$Q\rightarrow R$
And then assume Q to get R.
For reductio ad absurdum and arrow introduction I know that you have to discharge the assumptions that you use, I was just wondering if this is the case for assuming the antecedent.
Here is an argument that seems to require the assumption of the antecedents.
$E\rightarrow (\sim F \lor \sim (A \lor D)) \therefore E \land F \rightarrow \sim D \lor G$

You could do so, but the proof would be unfinished. You could discharge each premise in turn to get: 
$$P\implies [Q \implies R] \implies [P\implies [Q \implies R]]$$
If you introduced all of your premises at once, you could also prove:
$$[P\implies [Q \implies R] \land P \land Q] \implies  R$$
