This is from A Course in Arithmetic by JP Serre
ii) Let $p$ be a prime number and let $q = p^f(f \geq 1)$ be a power of $p$. Let be an algebraically closed field $\Omega$ of characteristic $p$. There exists a unique subfield $F_q$ of $\Omega$ which has $q$ elements. It is the set of roots of the polynomial$X^q-X$.
iii) All finite fields with $p^f$ elements are isomorphic to $F_q$.
The proof of the last part says
Assertion iii) follows from ii) and from the fact that all fields with $p^f$ elements can be embedded in $\Omega$, since $\Omega$ is algebraically closed.
Can someone explain me how iii) follows fom ii)?