Strictly Monotone Mapping with Totally Ordered Domain is Injective

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

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

Let $\phi: \struct {S, \preceq_1} \to \struct {T, \preceq_2}$ be a strictly monotone mapping.

Then $\phi$ is injective.

Proof
Hence the result.