reserve X,Y,Z,X1,X2,Y1,Y2 for set, x,y,z,t,x1,x2 for object,
  f,g,h,f1,f2,g1,g2 for Function;
reserve C,D,E for non empty set;
reserve c for Element of C,
  d for Element of D;
reserve f for Function of [:C,D:],E;

theorem
  for A,B,C being non empty set, f being Function of A, Funcs(B,C)
for a being Element of A, b being Element of B
      holds (uncurry f).(a,b) = f.a.b
proof
  let A,B,C be non empty set, f be Function of A, Funcs(B,C);
  let a be Element of A, b be Element of B;
  dom f = A & dom(f.a) = B by FUNCT_2:def 1;
  hence thesis by Th31;
end;
