Effective diagnosis of integrated circuits relies critically on the quality of diagnostic test vectors. Diagnostic test pattern generation aims at producing test vectors that distinguish between all distinguishable pairs of faults, and proving the remaining pairs of faults to be indistinguishable. Proving indistinguishabilities, much like proving undetectabilities in the case of detection-oriented test pattern generation, requires substantial computational effort. In this paper, we simplify the problem by showing that a significant number of indistinguishability relations can be proven implicitly, with little computational effort. Sequential indistinguishability is characterized and conditions for the identification of new indistinguishability relations based on already existing relations are established. Experiments on the ISCAS 89 benchmark circuits are presented to indicate the significant improvements achievable by the implicit identification of indistinguishabilities.