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 Th24:
 F|=A & F|=A=>B implies F|=B
 proof
  assume that
   A1: F|=A and
   A2: F|=A=>B;
  let M;
  assume A3: M|=F;
  let n be Element of NAT;
 (SAT M).[n,A=>B]=1 by Def12,A2,A3;
  then A4: (SAT M).[n,A]=>(SAT M).[n,B]=1 by Def11;
  (SAT M).[n,A]=1 by Def12,A1,A3;
  hence (SAT M).[n,B]=1 by A4;
 end;
