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I assume you mean the final expression for the electric force, which is indeed correct. John D has already pointed out the error in the derivation "fortuitously" giving the right answer.
I would merely point out that one can more easily get the answer by saying: F = QE where Q = charge on one plate and E=Q/2*A*eps0 is the field due to the other plate.
It would be wrong (by a factor of 2) to use the total E due to both plates. One plate does not exert a force on itself. -Carl