Add partial pressures:
P
1
=
n
1
RT/V
P
2
=
n
2
RT/V
P =
P
1
+
P
2
= (
n
1
+
n
2
)RT/V
Add moles of each substance:
n =
n
1
+
n
2
P = nRT/V = (
n
1
+
n
2
)RT/V