If an odd number is subtracted from an odd number, then the remainder is even.

Let the odd number *BC* be subtracted from the odd number *AB.*

I say that the remainder *CA* is even.

Since *AB* is odd, subtract the unit *BD,* therefore the remainder *AD* is even. For the same reason *CD* is also even, so that the remainder *CA* is also even.

Therefore, *if an odd number is subtracted from an odd number, then the remainder is even.*

Q.E.D.