Absorbing the structural rules in the sequent calculus with additional atomic rules

We show that if the structural rules are admissible over a set $$\mathcal{R}$$ of atomic rules, then they are admissible in the sequent calculus obtained by adding the rules in $$\mathcal{R}$$ to the multisuccedent minimal and intuitionistic $$\mathbf{G3}$$ calculi as well as to the classical one. Two applications to pure logic and to the sequent calculus with equality are presented.