# Isomorphism extension theorem

The theorem states that given any field $F$, an algebraic extension field $E$ of $F$ and an isomorphism $\phi$ mapping $F$ onto a field $F'$ then $\phi$ can be extended to an isomorphism $\tau$ mapping $E$ onto an algebraic extension $E'$ of $F'$ (a subfield of the algebraic closure of $F'$).