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 Th8:
  for x being Element of X1 holds (Proj (f, y)). x = f.(x, y)
proof
  let x be Element of X1;
  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_5:22;
end;
