  This article shows yet another proof of NP=CoNP$. In a previous article, we
proved that NP=PSPACE and from it we can conclude that NP=CoNP immediately. The
former proof shows how to obtain polynomial and, polynomial in time checkable
Dag-like proofs for all purely implicational Minimal logic tautologies. From
the fact that Minimal implicational logic is PSPACE-complete we get the proof
that NP=PSPACE.
  This first proof of NP=CoNP uses Hudelmaier linear upper-bound on the height
of Sequent Calculus minimal implicational logic proofs. In an addendum to the
proof of NP=PSPACE, we observe that we do not need to use Hudelmaier
upper-bound since any proof of non-hamiltonicity for any graph is linear
upper-bounded. By the CoNP-completeness of non-hamiltonicity, we obtain NP=CoNP
as a corollary of the first proof. In this article we show the third proof of
CoNP=NP, also providing polynomial size and polynomial verifiable certificates
that are Dags. They are generated from normal Natural Deduction proofs, linear
height upper-bounded too, by removing redundancy, i.e., repeated parts. The
existence of repeated parts is a consequence of the redundancy theorem for a
family of super-polynomial proofs in the purely implicational Minimal logic. It
is mandatory to read at least two previous articles to get the details of the
proof presented here. The article that proves the redundancy theorem and the
article that shows how to remove the repeated parts of a normal Natural
Deduction proof to have a polynomial Dag certificate for minimal implicational
logic tautologies.
