A D1104: Binary relation structure $M = (X \times Y, f)$ is a surjective map if and only if

(1)	$\forall \, x \in X : \forall \, y, y' \in Y \, ((x, y), (x, y') \in f \quad \Rightarrow \quad y = y')$ (D358: Right-unique binary relation)
(2)	$\forall \, x \in X : \exists \, y \in Y : (x, y) \in f$ (D359: Left-total binary relation)
(3)	$\forall \, y \in Y : \exists \, x \in X : (x, y) \in f$ (D360: Right-total binary relation)

A D18: Map $f : X \to Y$ is surjective if and only if \begin{equation} \forall \, y \in Y : \exists \, x \in X : f(x) = y \end{equation}