 wac\(^*_X\): \({\exists f \inn 2^X} [{\forall x \inn X}\ {\exists y \inn 2}\ \phi(x,y)  \rightarrow  {\forall x \inn X}\ \phi(x,fx)]\) provided it is provable in IST that  \(\forall x[\phi(x,0) \rightarrow  \neg\phi(x,1)]\)