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Proposition: Set-Theoretical Meaning of Ordered Tuples

Let \(X\) be a set. If for $n\ge 1,$ two $n$-tuples $(x_1,\ldots,x_n)$ and $(y_1,\ldots,y_n)$ of elements of $X$ are equal, then $x_i=y_i$ for all $i=1,\ldots,n,$ formally

$$(x_1,\ldots,x_n)=(y_1,\ldots,y_n)\Rightarrow x_1=y_1\wedge \ldots \wedge x_n=y_n.$$

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References

Bibliography

1. Ebbinghaus, H.-D.: "Einführung in die Mengenlehre", BI Wisschenschaftsverlag, 1994, 3th Edition