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 mapping which is strictly monotone.

Then $$\phi$$ is injective.

Proof
$$ $$ $$ $$

Hence the result.