Naming it Cause and Effect is misleading; it makes it seem like bayes rule only applies when there is a causal relation somewhere. It also make the symmetry of the first line seem off. I would write the first line as

P(A and B are both true) = P (A is true) x P (B is also true, given that we know A is already true) = P (B is true) x P (A is also true, given that we know B is already true)