Proof of Pairs in the Graph of a Point of $\mathbb{R}^{n}$

By Euclidean Space $\mathbb{R}^n$: n-Tuples of Real Numbers with Their Componentwise Operations (ii), $x$ is a map $x:[n]\to\mathbb{R}$ with $x_{k}=x(k)$. Applying Maps between Classes: Values, Pairs, Extensionality, Restrictions, Constant Maps and Preimages (ii) with $F=x$, $A=[n]$, $B=\mathbb{R}$ and $u=k$ gives, for every set $v$,

$$(k,v)\in x\iff v=x(k)=x_{k}.$$