reserve A,B,p,q,r for Element of LTLB_WFF,
  M for LTLModel,
  j,k,n for Element of NAT,
  i for Nat,
  X for Subset of LTLB_WFF,
  F for finite Subset of LTLB_WFF,
  f for FinSequence of LTLB_WFF,
  g for Function of LTLB_WFF,BOOLEAN,
  x,y,z for set,
  P,Q,R for PNPair;

theorem Th3: {} LTLB_WFF |= A iff not 'not' A is satisfiable
  proof
    hereby
      assume
A1:   {}l |= A;
      assume 'not' A is satisfiable;
      then consider M,n such that
A2:   (SAT M).[n,'not' A] = 1;
A3:   M |= {}l;
      (SAT M).[n,A] = 0 by A2,LTLAXIO1:5;
      hence contradiction by A3,A1,LTLAXIO1:def 12;
    end;
    assume
A4: not 'not' A is satisfiable;
    assume not {}l |= A;
    then consider M such that
    M |= {}l and
A5: not M |= A;
    consider n such that
A6: not (SAT M).[n,A] = 1 by A5;
    (SAT M).[n,'not' A] = 1 by A6,XBOOLEAN:def 3,LTLAXIO1:5;
    hence contradiction by A4;
  end;
