A special case of this fallacy that you often see is

Your Axioms (+ My Axioms) yield a bald contradiction. Therefore, your position isn't even coherent!

This is a special case of the fallacy because the charge of self-contradiction could stick only if the accused person really subscribed to both Your Axioms and My Axioms. But this is only plausible because of an implicit argument: "My Axioms are true, so obviously the accused believes them. The accused just hasn't noticed the blatant contradiction that results."