reserve p,q,r,s,A,B for Element of PL-WFF,
  F,G,H for Subset of PL-WFF,
  k,n for Element of NAT,
  f,f1,f2 for FinSequence of PL-WFF;
reserve M for PLModel;

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;then
    M |= A=>B by A2;
    then A4: (SAT M).A=>(SAT M).B=1 by Def11;
    M |= A by A1,A3;
    hence (SAT M).B=1 by A4;
  end;
