Identity Mapping is Left Identity

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.

Also see

 * Identity Mapping is Right Identity


 * Diagonal Relation is Left Identity
 * Diagonal Relation is Right Identity