reserve a,b,c for boolean object;
reserve p,q,r,s,A,B,C for Element of LTLB_WFF,
        F,G,X,Y for Subset of LTLB_WFF,
        i,j,k,n for Element of NAT,
        f,f1,f2,g for FinSequence of LTLB_WFF;
reserve M for LTLModel;

theorem
  F|-p=>q implies F\/{p}|-q
 proof
  p in {p} by TARSKI:def 1;
  then p in F\/{p} by XBOOLE_0:def 3;
  then A1: F\/{p}|-p by Th42;
  assume F|-p=>q;
  then F\/{p}|-p=>q by Th56;
  hence F\/{p}|-q by A1,Th43;
 end;
