Double integral of the product of Dirac delta functions

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I'm curious how one would proceed in integrating a function of the form -

$$ \iint dx \hspace{1mm} dx' \hspace{1mm} \delta(x - x') \delta(x' - x) f(x, x') $$

My intuition (and the solution to the problem, which is given) tells me that the answer is -

$$ f(x', x) $$

but I'm having trouble convincing myself. Thanks