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
  F |- A => B implies F \/ {A} |- B
 proof
    A in {A} by TARSKI:def 1;
    then A in F\/{A} by XBOOLE_0:def 3;
    then A1: F\/{A}|-A by th42;
    assume F|-A=>B;
    then F\/{A}|-A=>B by monmp,XBOOLE_1:7;
    hence F\/{A}|-B by A1,th43;
  end;
