Extended independence-friendly (IF) logic is an extension of classical first-order logic. The main characteristic of IF logic is to allowing one to express independence relations between quantifiers. However, its propositional level has never been successfully axiomatized. Based on Cirquent calculus, this paper axiomatically constructs a formal system, which is sound and complete w.r.t. the propositional fragment of Cirquent-based semantics, for propositional extended IF logic. Such a system can account for independence relations between propositional connectives, and can thus be considered an axiomatization of purely propositional extended IF logic in its full generality.