This is Exercise 5.1.F from Vakil's notes:
Exercise 5.1.F. Show that a scheme is quasiseparated if and only if the intersection of any two affine open subsets is a finite union of affine open subsets, if and only if the intersection of any two quasicompact open subsets is a quasicompact open subsets.
The statements 1 $\implies$ 2 and 2 $\implies 1$ are easy to prove. I think I am missing something. Isn't statement 3 the definition of quasiseparatedness? Here is the definition right above this exercise:
A topological space is quasiseparated if the intersection of any two quasicompact open sets is quasicompact.
So there is nothing to prove for statement 3, right? Thank you for your help!