Double slash is part of if but only if if I remember correctly. A B is equivalent to /A /B.
Here is the lesson http://7sage.com/lesson/advanced-bi-conditionals/
if A then neither B nor C means A -> /B AND A->/C so if B or C (either of the two) are present, then A can't be - so you're right. I may be wrong... but that is my understanding of it. I think there is a lesson in advanced logic on this.