Definition:Injection/Definition 3

Definition
Let $f$ be a mapping.

Then $f$ is an injection :
 * $f^{-1} {\restriction_{\Img f} }: \Img f \to \Dom f$ is a mapping

where $f^{-1} {\restriction_{\Img f} }$ is the restriction of the inverse of $f$ to the image set of $f$.

Also see

 * Equivalence of Definitions of Injection