reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem Th2:
  for f,g,h being Function st f \/ g = h
   for x being object st x in dom f /\ dom g holds f.x = g.x
proof
  let f,g,h be Function such that
A1: f \/ g = h;
  let x be object;
  assume
A2: x in dom f /\ dom g;
  then x in dom f by XBOOLE_0:def 4;
  then
A3: h.x = f.x by A1,GRFUNC_1:15;
  x in dom g by A2,XBOOLE_0:def 4;
  hence thesis by A1,A3,GRFUNC_1:15;
end;
