The law of contradiction is provable from the remaining axioms of the intuitionistic system H without taking it as a primitive.

Griss contested Brouwer’s use of negation, objecting to both the law of contradiction and ex falso. It is worth noting that negation is not really needed for intuitionistic mathematics since \(0 = 1\) is a known contradiction so \(\neg A\) can be defined by \(A \rightarrow 0 = 1.\) Then ex falso can be stated as \(0 = 1 \rightarrow A,\) and the law of contradiction is provable from the remaining axioms of \(\mathbf{H}.\)