How to use Dirac delta sifting property to prove question?

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For my own understanding, how do I prove this equation using the Dirac delta sifting property?

Equation to prove: (A)*delta(t-to) + (B)*delta(t-to) = (A+B)*delta(t-to)

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It is just the distributive property. Whatever $\delta(t-t_0)$ is (I know, but it doesn't matter here) the equation is true. You don't need the shifting property.