  We derive new bounds on higher-dimension operator coefficients in
four-dimensional Einstein-Maxwell theory. Positivity of classically-generated
corrections to the Wald entropy of thermodynamically stable, rotating dyonic
black holes implies a multiparameter family of field basis invariant
inequalities that exhibit electromagnetic duality and are satisfied by examples
from field and string theory. These bounds imply that effective operators
modify the extremality condition of large black holes so as to permit their
decay to smaller ones, thus satisfying the weak gravity conjecture.
