Image is Subset of Codomain/Corollary 2
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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.
$\blacksquare$