This is the second half of DeMorgan’s Law (also known as DeMorgan’s Rule or DeMorgan’s Theorem), which remains the most important replacement rule in logic. Here, the law says that P v Q is equivalent to ~(~P ^ ~Q). It is really useful once again because it makes excessively complicated conjunctions with tons of negations into a very clean disjunction.

The rule is named after Augustus De Morgan, a 19th Century British mathematician.