Bourbaki: Use of tau choice operator?

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I have a question about evaluating truth of the sign assemblies in Bourbaki Theory of Sets.

It's my understanding that when there are duplicate assemblies each starting with the choice operator $\tau$, this operator must choose the same value for each linked $\square$ in all duplicate assemblies. Therefore, to evaluate the truth of a sequence of signs, the sequence must be searched for duplicate sequences starting with $\tau$.

Is it documented elsewhere? I suspect this is costly, but are there advantages? Perhaps eliminating the variable name from the form so duplicates can be found?

I have yet to see any Bourbaki documentation on this and am confused by that.