Counting through Bijections, Injections and Surjections

In the setting of Routine Facts Used Without Citation: Arithmetic, Maps, Predicativity and Indices, let $A$ and $B$ be sets and $f:A\to B$ a map, let finite sets be as in Finite Sets (i) and $\#$ as in The Number of Elements of a Finite Set (i).

(i) Bijections. If $f$ is bijective and $A$ is finite, then $B$ is finite and $\#B=\#A$.

(ii) Injections. If $f$ is injective and $B$ is finite, then $A$ is finite and $\#A\le\#B$.

(iii) Surjections. If $f$ is surjective and $A$ is finite, then $B$ is finite and $\#B\le\#A$.