Everything in math stems from definitions. Eg: Let an 'implication' be defined as ...
But any such 'let' actually means 'if it be true that'.
So what we're really saying is 'If an implication be defined as ..., Then ...'
Hence, all definitions are of the form of an implication itself. Does that mean, we actually define an implication using an implication itself?
In mathematics, the notion of a definition is an informal one. There is no formal distinction between statements that are definitions and those that are not, so the following are only suggested guidelines.
Definitions can tell us what a word means. Such definitions are usually stated as a bi-conditional, e.g. function $f$ is defined to be continuous at point $x\in \mathbb{R}$ if and only if...
They can also list the essential features of some logical structure(s), e.g. the Peano axioms for the set of natural numbers.
A recursive definition defines one structure in terms that mention that same structure, e.g. the factorial function (the $!$-operator):
$0!=1$
$ x!= (x-1)! \cdot x$, if $x\in \mathbb{ N}^+$
Note that in the last line, we have the $!$-operator on both sides of the equality.