Help me proving Dalton's law of partial pressure formula
After having some discussion with @JohnRennie 

Let $P_i=n_i \dfrac{RT}{V}$ then $P_i=\dfrac{n_i}{n_{\text{total}}}\dfrac{n_{\text{total}}RT}V$

$P_i=x_i P_{\text{total}}$

Where $x_i$ is mole fraction of $i^{\text{th}}$ particle.