How to write the net ionic equation for barium bromide plus hydrochloric acid?

BaBr2(aq) + 2HCl(aq) ---> BaCl2(aq) + 2HBr(aq)

I am not sure if I did the total ionic equation right because they all cancel out.

Ba^2+(aq) + 2Br^-(aq) + 2H^+(aq) + 2Cl^-(aq) ---> Ba^2+(aq) + 2Cl^-(aq) + 2H^+(aq) + 2Br^-(aq)
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