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

A comment on the enhancement of global symmetries in superconformal SU(2) gauge theories in 5D