This is a property listed on MathWorld:
One nice property of an Abelian extension $K$ of a field $F$ is that any intermediate subfield $E$, with $F \subset E \subset K$, must be a Galois extension field of $F$ and, by the fundamental theorem of Galois theory, also an Abelian extension
What specifically about the fundamental theorem of Galois Theory shows that? To my knowledge, it only shows a one-to-one correspondence from the Galois subgroups and the intermediate fields. How does that make it abelian?