reserve a,b,c,d for Ordinal;
reserve l for non empty limit_ordinal Ordinal;
reserve u for Element of l;
reserve A for non empty Ordinal;
reserve e for Element of A;
reserve X,Y,x,y,z for set;
reserve n,m for Nat;

theorem Th6:
  for f being Function st f is_isomorphism_of RelIncl X, RelIncl Y
  for x,y st x in X & y in X holds x c= y iff f.x c= f.y
  proof
    let f be Function; assume
A1: f is_isomorphism_of RelIncl X, RelIncl Y;
    let x,y such that
A2: x in X & y in X;
A3: field RelIncl X = X & field RelIncl Y = Y by WELLORD2:def 1; then
    dom f = X & rng f = Y by A1; then
A4: f.x in Y & f.y in Y by A2,FUNCT_1:def 3;
    x c= y iff [x,y] in RelIncl X by A2,WELLORD2:def 1; then
    x c= y iff [f.x,f.y] in RelIncl Y by A1,A2,A3;
    hence thesis by A4,WELLORD2:def 1;
  end;
