If X_m, X_p and X_V represent mole, pressure and volume fractions respectively, then

$$\begin{gathered} n_1=\text{ moles of component I }\frac{p_1{V}_1}{R{T}_1}=\frac{p_1{V}_1}{RT} \\ {n}_2=\text{ moles of component II }\frac{p_2{V}_2}{R{T}_2}=\frac{p_2{V}_2}{RT} \\ {X}_m\text{ (of component I) }=\frac{n_1}{n_1+n_2}=\frac{p_1{V}_1}{p_1{V}_1+p_2{V}_2} \\ =\frac{V_1}{V_1+V_2}=X_V\text{ at constant }p \\ =\frac{p_1}{p_1+p_2}=X_p\text{ at constant }V \\ Hence, X_m=X_V=X_p \end{gathered}$$