Field Product with Non-Zero Element yields Unique Solution

Theorem
Let $\struct {F, +, \times}$ be a field whose zero is $0_F$ and whose unity is $1_F$.

Let $a, b, x \in F$ such that $b \ne 0_F$.

Let:
 * $b \times x = a$

Then:
 * $x = a b^{-1}$

That is:
 * $x = \dfrac a b$

where $\dfrac a b$ denotes division.