Inverse of Injection is One-to-One Relation

Theorem
Let $f$ be an injective mapping.

Then its inverse $f^{-1}$ is a one-to-one relation.

Proof
We are given that $f$ is an injective mapping.

Hence by definition $f$ is a one-to-one relation.

The result follows from from Inverse of One-to-One Relation is One-to-One.