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

Theorem
Let $\struct {S, \preceq_1}$ be a totally ordered set.

Let $\struct {T, \preceq_2}$ be an ordered set.

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

Then $\phi$ is an order embedding. 