
theorem Th1:
  for X,x being set,
      F being Function of [:X,X:],X st
    x in [:X,X:] holds F.x in X
proof
  let X,x be set;
  let F be Function of [:X,X:],X;
A1: dom F = [:X,X:] by PARTFUN1:def 2;
  assume x in [:X,X:];
  then rng F c= X & F.x in rng F by A1,FUNCT_1:def 3,RELAT_1:def 19;
  hence thesis;
end;
