  Recently, the superconformal index for a class of 5-dimensional
superconformal quantum field theories with gauge group SU(2) and $N_f$ flavors
was computed in Kim, Kim, and Lee (2012) to a few low orders in the chemical
potential and enhancement of the global symmetry to $E_{N_f+1}$ was confirmed
to this low order. In this note I provide an argument that the information
contained in these few low order terms in the expansion of the index is
sufficient to prove the enhancement of global symmetries in the theories. So,
in particular the expression for the indices must display the enhancement to
all orders in the chemical potential.
