Full Idea
The standard requirement of definitions involves 'eliminability' (any defined terms must be replaceable by primitives) and 'non-creativity' (proofs of theorems should not depend on the definition).
Gist of Idea
Definitions should be replaceable by primitives, and should not be creative
Source
James Robert Brown (Philosophy of Mathematics [1999], Ch. 7)
Book Reference
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.94
A Reaction
[He cites Russell and Whitehead as a source for this view] This is the austere view of the mathematician or logician. But almost every abstract concept that we use was actually defined in a creative way.