An inequality based on conditional independence of resampling

Question

Suppose we have i.i.d. samples $X_1,X_2,...,X_n$ and $Y_1,Y_2,...,Y_{K_n}$ comes from resampling from $X$ with replacement, $K_n\leq n$. Can we say that $Y_1,Y_2,...,Y_{K_n}$ are i.i.d conditional on $X_1,X_2,...,X_n$, and use the Dvoretzky-Kiefer-Wolfowitz inequality to get: $$P\left(\left|\frac{1}{K_n} \sum_{i=1}^{K_n} 1(Y_i \leq 0 )-\frac{1}{n} \sum_{i=1}^{n} 1(X_i \leq 0 )\right|\geq \sqrt{\frac{log(2n)}{2K_n}}\right)\leq \frac{1}{n} $$