From Wikipedia: "Emil Post proved that a set of logical connectives is functionally complete if and only if it is not a subset of any of the following sets of connectives: ..." I don't remember if I studied the proof, but I would guess that the hard part is to prove the "if" part, i.e., not being a subset implies completeness. Your set of connectives is one of the five listed in the theorem, and once you know the name of this set, it is easy to see that it isnotcomplete.