Comment by memkit

Your last statement is misleading. A problem being NP-complete isn't exactly the property that allows you to reduce any NP problem to it. Suppose there was a complexity class MP-hard that has no efficient reduction to an NP-complete problem. Then a problem being MP isn't what allows me to write a reduction to the MP-hard problem; I could just as easily write a reduction from a problem in P to the MP-hard problem. Your statement is misleading but incidentally correct because the true condition (NP-hard or easier) happens to be equivalent to your stated condition (NP) for this particular complexity class. It would be clearer to simply state that you can always reduce an easy problem to a harder one.