We can restate Dalton's Law using mole fractions. The partial pressure of any substance in a gas mixture is the mole fraction of that substance times the total pressure.
\[ \eqalign{
P_i &= {{n_i}RT\over{V}} \cr
&={n_{\rm total}\over n_{\rm total}}\left({{n_i}RT\over{V}}\right) \cr
&= {{n_i}\over n_{\rm total}}\left({{n_{\rm total}RT}\over{V}}\right) \cr
&={{n_i}\over n_{\rm total}}\left({P_{\rm total}}\right) \cr
&=X_i P_{\rm total} \cr } \]
\[P_i = X_i P_{\rm total}\]