[gizmo686]

> I remember reading that if you need the CH to prove something, then you should definitely reconsider the statement you are trying to prove

This is not entirely true. There are many proofs that begin by assuming CH. There are also two ways of interpreting "need CH to prove". One way is that the thing you are trying to prove is equivalent to CH, which is an interesting/useful result. Another way to interpret it is that you can not come up with another way of proving it. In the latter case, the CH based proof justifies that your proposition is not inconsistent, and may even lead you (or others) to proof that it is true regardless of CH. If I recall correctly some statements have been proved by proving the statement when CH is true, and also when CH is false.