In a gaseous mixture, the pressure exerted by a component, #P_A#, is the same as the pressure it would exert if it ALONE occupied the container. The total pressure is the sum of the individual partial pressures.
#P_"Total"# #=# #P_A + P_B + P_C + P_D........#
And if we assume ideality,
#=# #(n_ART)/V+(n_BRT)/V+(n_CRT)/V+(n_DRT)/V+#
Thus, #P_"Total"# #=# #(RT)/V{n_A + n_B + n_C + n_D + }#
And #P_A# #=# #(RT)/Vxxn_A/{n_A + n_B + n_C + n_D + }#
Thus the partial pressure #P_Aprop"Mole fraction of Gas A"#, with the constant of proportionality #(RT)/V#.