1. The pressure, the force applied is directly proportional to its magnitude, that receives the area.
   P α F……….. (i)
2. The force that gives pressure is inversely proportional to the area that receives the force.
   P α 1/A ………….. (ii)

From equation (i) and (ii) we get,
P α F/A

or, P = K (F/A) , where K= constant

If 1 N force is applied in 1 square meter area, then the pressure will be 1N/m² and thus, k=1.

Then, 

P=F/A. Proved.