 reserve T for Ternary_Boolean_Algebra;
 reserve a,b,c,d,e for Element of T;
 reserve x,y,z for Element of T;

theorem Th33: :: Theorem 3.3
  Tern (a,b,Tern (c,b,d)) = Tern(Tern(a,b,c),b,d)
proof
  set b1 = Tern (a,b,c);
  set b2 = Tern (a,b,d);
  Tern (a,b,Tern (c,b,d)) = Tern (b1,b,b2) by TDis
     .= Tern(Tern(b1,b,a),b, Tern(b1,b,d)) by TDis
     .= Tern(b1,b, Tern(b1,b,d)) by Lemma33
     .= Tern(Tern(b1,b,b`),b,Tern(b1,b,d)) by TRADef
     .= Tern(b1,b,Tern(b`,b,d)) by TDis
     .= Tern(b1,b,d) by TLADef;
  hence thesis;
end;
