The following theorem is proved in EGA IV 2.4.6:

Every morphism of schemes, which is flat and locally of finite presentation, is open.

I've already seen some applications of this theorem, so I want to understand the proof. But it is based on the whole theory of (ind)constructible sets, whose development seems to be quite long and (sorry!) uninteresting in EGA.

So I want to know: Is it possible to give a direct proof? We may reduce to the affine case, so perhaps it's an observation from commutative algebra?