Image is Subset of Codomain/Corollary 2

Corollary of Image is Subset of Codomain

Let $f: S \to T$ be a mapping.

For all subsets $A$ of the domain $S$, the image of $A$ is a subset of the codomain of $f$:

$\forall A \subseteq S: f \sqbrk A \subseteq T$

Proof

As a mapping is by definition also a relation, the result follows immediately from Image is Subset of Codomain.

$\blacksquare$