Condition notation: all variables must all be zero or all not be zero

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To be or not to be...

What is a good mathematical notation of the criterion, that all variables in an equation must all be zero (or whatever value) or all not be zero (or whatever value)?

On the internet I couldn't find anything that would answer my question. Example of what I think it would look like: $$y = f(x, u, i)$$ $$x, u, i \neq 0 \text{ or } x, u, i = 0$$

Hope to hear from you.

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"Either $x,u,i$ are all zero or none of them is zero."

Alternatively, "Either $x=u=i=0$ or $xui\neq0.$" But I think this is not as clear as simply saying what you mean.

Not everything has to be a notation.