Definition of Quick Subfield Theorem

Let $F$ be a field and $K$ a subset of $F$. Then $K$ is a subfield of $F$ if and only if:

1. $K$ contains the zero and the unity of F,
2. if $a,b\in L$ then $a+b$ and $ab$ belong to $K$,
3. if $a\in K$ then $-a\in K$,
4. if $a\in K$ and $a\ne 0$ then $a^{-1}\in K$.