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

theorem
  x =01=> y & y ==> z implies x =*=> z
  proof
    assume
A1: x =01=> y;
    assume
A2: y ==> z;
A3: x =*=> y by A1,Lem1;
A4: y =*=> z by A2,Th2;
    thus x =*=> z by A3,A4,Th3;
  end;
