reserve fi,psi for Ordinal-Sequence,
  A,A1,B,C,D for Ordinal,
  X,Y for set,
  x,y for object;

theorem
  A c= B implies A-^C c= B-^C
proof
  assume
A1: A c= B;
A2: now
    assume
A3: C c= A;
    then
A4: A = C+^(A-^C) by Def5;
    C c= B by A1,A3;
    then C+^(A-^C) c= C+^(B-^C) by A1,A4,Def5;
    hence thesis by Th23;
  end;
  not C c= A implies thesis by Def5;
  hence thesis by A2;
end;
