This paper offers arguments for the provable security of a class of ID-based signature schemes called ID-based generic signature schemes in the random oracle model. The theoretical result can be viewed as an extension of the Forking Lemma due to Pointcheval and Stern for ID-based signature schemes, and can help to understand and simplify the security proofs of previous work such as Cha-Cheon's scheme, Hess's scheme-1, Cheon-Kim-Yoon's scheme, and so on.