Strictly Monotone Mapping with Totally Ordered Domain is Injective

Theorem
Let $\left({S, \preceq_1}\right)$ be a totally ordered set.

Let $\left({T, \preceq_2}\right)$ be a poset.

Let $\phi: \left({S, \preceq_1}\right) \to \left({T, \preceq_2}\right)$ be a strictly monotone mapping.

Then $\phi$ is injective.

Proof
Hence the result.