Hello !

define relation this way:

It is easy to verify that is an equivalence relation and that .

Then consider an arbitrary equivalence relation such that and, again easily, show that .

So, you showed that~!! (and this answers your question).

note:

Definition of~that you gave is sometimes called 'definition from above', while definition I gave for is called 'definition from below'. The claim you are proving states that they are equivalent.