Let $f : A \to B$ be a finite flat map of (commutative) rings. It is a known consequence of Chevalley's theorem (on constructible sets) that the induced map $Spec B \to Spec A$ is open.

The Stacks Project (Tag 00FE) proves Chevalley's theorem in various steps, including a reduction to the case mentioned above.

My question: is there a quick, independent argument showing that a finite flat map is open?

Let $f : A \to B$ be a finite, finitely presented, flat map of (commutative) rings. It is a known consequence of Chevalley's theorem (on constructible sets) that the induced map $Spec B \to Spec A$ is open.

The Stacks Project (Tag 00FE) proves Chevalley's theorem in various steps, including a reduction to the case mentioned above.

My question: is there a quick, independent argument showing that a finite, finitely presented, flat map is open?