  We consider constrained-degree percolation model on the hypercubic lattice
\linebreak $\mathbb{L}^d=(\mathbb{Z}^d,\mathbb{E}^d)$. In this model, there
exits a sequence $(U_e)_{e\in\mathbb{E}^d}$ of i.i.d. random variables with
distribution $Unif([0,1])$ and a positive integer $k$, which is called a
constraint. Each edge $e$ attempts to open at time $U_e$, and the attempt is
successful if the number of neighboring edges open at each endvertex of $e$ is
at most $k-1$. In \cite{hartarsky2022weakly}, the authors demonstrated that
this model undergoes a phase transition when $d\geq3$ and for most nontrivial
values of $k$. In the present work, we prove that, for any fixed constraint,
the number of infinite clusters at any given time $t\in[0,1)$ is either 0 or 1,
almost surely.
