In classical logic, the universal negative is one of the four types of categorical proposition. The universal negative states that no member of a class is a member of another given class. In other words, No X are Y.
No monkeys eat soy.
No noders are neurotic.
The universal negative also implies its converse. From the examples above, we know that nothing that eats soy is a monkey and nobody who is neurotic nodes.
The rule You cannot prove a universal negative is sometimes invoked against atheists, but this is false (as well as being a universal negative itself!). Provable universal negatives include