I don't really agree. I find the long-winded version confusing, and as I am not sure if there is a gotcha somewhere in there, I have to read the whole thing and follow the whole argument. You don't necessarily have to use math symbols, but it really helps to be terse.
For anyone with even a passing knowledge of symbolic logic, what you provided is clear. But the explanation wouldn't be required for those people who are going to be familiar with that Fallacy anyway. It's for those who aren't aware of it. In that case, the symbolic version is of no help and the longer verbal explanation is important.
Agreed! I considered writing something along the lines of what you wrote, but I don't think most people would understand it who haven't already studied at least some logic.