Odd Number minus Odd Number is Even

Theorem

 * If from an odd number an odd number be subtracted, the remainder will be even.

Proof
Let $a$ and $b$ be odd numbers.

Then by definition of odd number:
 * $\exists c \in \Z: a = 2 c + 1$
 * $\exists d \in \Z: b = 2 d + 1$

So:

Hence the result by definition of even number.