Others are often given by adding one or more axioms to Examples include: Generalized variants of the above (but actually equivalent principles over intuitionistic logic) are, respectively, This list is, for the most part, not any sort of ordering.
For example, as with WPEM and De Morgan's law, several forms of DGP using conjunction may be expressed.
It may also be worth noting that, taking all of intuitionistic logic for granted, the equalities notably rely on explosion.
For example, over mere minimal logic, as principle PEM is already equivalent to Consequentia mirabilis, but there does not imply the stronger DNE, nor PP, and is not comparable to DGP.
Note that if a consistent theory validates WPEM but still has independent statements when assuming PEM, then it cannot have DP.
Given a Heyting algebra H, the set of propositional formulas that are valid in H is an intermediate logic.