This addendum supplies details of the proof in 3.6 of our paper Disjunction and existence under implication in elementary intuition-istic formalisms in this Journal, vol. 27 (1962), pp. 11–18, as promised in Footnote 8 of that paper (p. 16 lines 11 and 16, for “├” read “|”).A congruence-substitution (or free substitution with change of bound variables) on a formula E with result F consists in, simultaneously, substituting for each of the free variables of E in all its free occurrences a respective term and replacing each bound occurrence of a variable in E by a respective variable, so that (a) each image in F of a free occurrence of a variable in E is free (IM p. 410) and (b) each image in F of a bound occurrence of a variable in E is bound by the corresponding quantifier (i.e. if the j-th quantifier in E binds the original occurrence, then the j-th quantifier in F binds the image).