Identity Mapping is Left Identity/Proof 2

Theorem

Let $S$ and $T$ be sets.

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

Then:

$I_T \circ f = f$

where $I_T$ is the identity mapping on $T$, and $\circ$ signifies composition of mappings.

Proof

By definition, a mapping is also a relation.

Also by definition, the identity mapping is the same as the diagonal relation.

Thus Diagonal Relation is Left Identity can be applied directly.

$\blacksquare$