Abstract
In this paper, we deal with a relationship among the law of excluded middle, the double negation elimination and the independence of premiss rule ( $$\mathrm {IPR}$$ ) for (many-sorted) intuitionistic predicate logic. After giving a general machinery, we give, as corollaries, several examples of extensions of $$\mathbf {HA}$$ and $$\mathbf {HA}^\omega $$ which are closed under $$\mathrm {IPR}$$ but do not derive the independence of premiss axiom.
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