The de Jongh property for Basic Arithmetic

We prove that Basic Arithmetic, BA, has the de Jongh property, i.e., for any propositional formula A(p ₁,..., p _n ) built up of atoms p ₁,..., p _n , BPC ({vdash}) A(p ₁,..., p _n ) if and only if for all arithmetical sentences B ₁,..., B _n , BA ({vdash}) A(B ₁,..., B _n ). The technique used in our proof can easily be applied to some known extensions of BA.