Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing/Reverse Implication

Theorem
Let $\left({S, \preceq_1}\right)$ be a totally ordered set and let $\left({T, \preceq_2}\right)$ be a poset.

Let $\phi: S \to T$ be a strictly increasing mapping.

Then $\phi$ is an order embedding

