reserve A,B,C,D,p,q,r for Element of LTLB_WFF,
        F,G,X for Subset of LTLB_WFF,
        M for LTLModel,
        i,j,n for Element of NAT,
        f,f1,f2,g for FinSequence of LTLB_WFF;

theorem th15:
  A in LTL_axioms implies F|-0 A
  proof
    assume A in LTL_axioms;then
    'G' A in LTL0_axioms;then
    F|-0 'G' A by th10;
    hence F|-0 A by th9;
  end;
