reserve X1, X2, Y for non empty RelStr,
  f for Function of [:X1, X2:], Y,
  x for Element of X1,
  y for Element of X2;

theorem Th7:
  for y being Element of X2 holds (Proj (f, x)). y = f.(x, y)
proof
  let y be Element of X2;
  dom f = the carrier of [:X1, X2:] by FUNCT_2:def 1
    .= [:the carrier of X1, the carrier of X2:] by YELLOW_3:def 2;
  then [x,y] in dom f by ZFMISC_1:87;
  hence thesis by FUNCT_5:20;
end;
