Is proving both sides of iff necessary? I have always been taught to prove both ways of an "if and only if" statement in a formal proof, but if the opposite way is very similar to the proof of the first way. Can you just leave a note and leave it at that?
 A: Quite generally, in a mathematical proof we often need to establish a number of cases in turn, and sometimes it can be that two or more of these cases can  be proved similarly. Then, sure, so long as the cases are indeed similar, and you aren't a complete beginner, you can write after your proof of case (a) the likes of "Case (b) is proved similarly" -- if (but only if) the proof is genuinely much the same apart from tweaks that will be obvious to anyone who can follow the proof for case (a). [I'd say that you shouldn't get marked down for this in homework: on the contrary, you should get credit for spotting the proofs for (a) and (b) are much the same.]
What applies in general can in principle apply in the particular case where the two cases we need to look at are the two directions of biconditional. If the "if" and "only if" directions can indeed be proved very similarly, then of course it is fine to say so (again assuming you are not a complete beginner, when it best to spell out everything). But be warned, this isn't at all the typical case for a biconditional. So be very careful indeed before allowing yourself the short cut of saying that the second direction of the biconditional is proved similarly to the first. 
