Deveno seems correct in everything he wrote. I don't understand your argument against it. Here is an expanded proof (the second part is not necessary, but maybe it will better explain things).

Assume

. Choose any

. Then

. This gives

, so according to the implication we assumed,

. Next, choose any

. Now, the implication is not relevant since we only care when

. So, we don't have to use every possible value for

. We are showing that given that implication, we can arrive at the conclusion that

. We can have

, and the implication is still true. It is simply not relevant.