Definition:Bijection/Definition 5

Definition
A relation $f \subseteq S \times T$ is a bijection :
 * $(1): \quad$ for each $x \in S$ there exists one and only one $y \in T$ such that $\left({x, y}\right) \in f$
 * $(2): \quad$ for each $y \in T$ there exists one and only one $x \in S$ such that $\left({x, y}\right) \in f$.

Also see

 * Equivalence of Definitions of Bijection


 * Injection is Bijection iff Inverse is Injection