The Empty Set and The Concept of Nothingness

There's a funny proof (can't say I completely agree with this one) that any set contains the empty set.
It uses a couple of proposition logic rules:

1) let x belongs to the empty set
2) if this is so, then it must be true that x belongs to A (using the next property: if p is false, then q)
3) the step #1 is false, so x belongs to A
4) x = the empty set (using the next property: if x is any set, then x is also the empty set).

We can generalize that proof into the next, using this determination:

b) amongs all the possible sets there's a set that = the concept of nothingness
4') x = {the set that is the concept of nothingness}
c) if there's an empty set, therefore there's a concept of nothingness