reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem
  x in f"Y iff [x,f.x] in f & f.x in Y
proof
  thus x in f"Y implies [x,f.x] in f & f.x in Y
  proof
    assume x in f"Y;
    then ex y being object st [x,y] in f & y in Y by RELAT_1:def 14;
    hence thesis by FUNCT_1:1;
  end;
  thus thesis by RELAT_1:def 14;
end;
