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

theorem Lem5a:
  x <==> y & y <=*=> z implies x <=*=> z
  proof
    assume
A1: x <==> y;
    assume
A2: y <=*=> z;
A3: x <=*=> y by A1,Th6;
    thus x <=*=> z by A3,A2,Th7;
  end;
