Uuuhhhh, wait, there’s something wrong with your post. A simple logical statement can imply a complex-looking logical statement, right? Imagine that C is a very simple statement that implies B which is very complex. Then A∩B∩C is logically equivalent to A∩C, which is simpler than A∩B because C is simpler than B by assumption. Whoops.
Uuuhhhh, wait, there’s something wrong with your post. A simple logical statement can imply a complex-looking logical statement, right? Imagine that C is a very simple statement that implies B which is very complex. Then A∩B∩C is logically equivalent to A∩C, which is simpler than A∩B because C is simpler than B by assumption. Whoops.