reserve X for ARS, a,b,c,u,v,w,x,y,z for Element of X;

theorem
  x <=01= y or x <==> y implies x <=01=> y
  proof
    assume
A1: x <=01= y or x <==> y;
A3: x <==> y or x = y by A1;
    thus x <=01=> y by A3;
  end;
