In the context of PDL, the two rules of consequence are in fact special cases of the rule of composition. To obtain the first rule, substitute α1 with α and α2 with skip. To obtain the second rule, substitute α1 with skip and α2 with α. It suffices to apply the axiom schema (A4), and to remark that [α;skip]A ↔ [α]A and [α;skip]A ↔ [α]A are also ⊢-deducible for all A and all α. 