Not all the steps are correct.
Your first step needs to be
That's essentially a DeMorgan Law application. You fix this error, incidentally, in the next step.
Also, you should be more careful with your parentheses here:
In context, I can tell that you meant
but you don't want to write so that people can understand. Write so that no one can misunderstand!
All your steps are reversible, correct? So just change your implications to double implications, and you can then omit the sentence "And the reverse is true." (You mean converse, by the way.)
As Strunk and White have told us, "Omit needless words!"