The notion of fuzzy implication plays the central role in this paper, an iterative Boolean-like law with fuzzy implications being analyzed. The authors study some classes of fuzzy implications satisfying the relation \[ I(x,y)=I(x,I(x,y)) \quad \forall (x,y)\in [0,1]^{2},\tag{1} \] which is an extension of the Boolean law \(p\rightarrow (p\rightarrow q)=p\rightarrow q\) from classical logic to fuzzy logic. The definitions and some basic properties of fuzzy negations, t-norms, t-conorms are presented in Section 2. In Section 3, the authors give the definition and some general properties of fuzzy implications; a table of the most used implications and their properties is also presented. In Section 4, in order to solve (1), three classes of fuzzy implications generated by a t-norm \(T\), a t-conorm \(S\) and a fuzzy negation \(n\) are studied; these are \(S\)-implication, \(R\)-implication and \(QL\)-implication, defined, for all \(x,y \in [0,1]\), by \(I(x,y)=S(n(x),y)\), \(I(x,y)= \sup\{z\in [0,1]\mid T(x,z)\leq y\}\) and \(I(x,y)=S(n(x),T(x,y))\) respectively. The t-norm \(T_{M}(x,y)= \min(x,y)\) and the t-conorm \(S_{M}(x,y)= \max(x,y)\) play the most important role in the solution of (1). The obtained results can be synthesized in: an \(S\)-implication generated by a t-conorm \(S\) and a continuous fuzzy negation satisfies (1) iff \(S=S_{M}\); an \(R\)-implication generated by a left-continuous t-norm \(T\) satisfies (1) iff \(T=T_{M}\); a sufficient and not necessary condition for a \(QL\)-implication generated by a fuzzy negation, a t-norm \(T\) and a t-conorm \(S\), to satisfy (1) is \(T=T_{M}\) and \(S=S_{M}\). Sufficient and necessary conditions for a \(QL\)-implication generated by a strong negation and a pair (t-norm, t-conorm) of nilpotent (or expressed as ordinal sums) operators are given, too. The presentation is clear and easy to follow, and the topic is of interest for researchers involved in the fuzzy logic domain.