Condition for Difference of Field Elements to be Zero

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

Let $a, b \in F$

Then:
 * $a - b = 0_F$


 * $a = b$

where $a - b$ denotes subtraction.

Necessary Condition
Let $a = b$.

Then:

Sufficient Condition
Let $a - b = 0_F$.

Then: