University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic"
Study Theorem 1 (Algebraic rules for statement forms) on page Lo-3.
A similar argument could be used to prove DeMorgan's law, which is very useful and widely used in communication, mathematics, engineering, and the sciences. Please make sure to familiarize yourself with DeMorgan's law before moving on to other sections of this course.