reserve A,B,C,D,p,q,r for Element of LTLB_WFF,
        F,G,X for Subset of LTLB_WFF,
        M for LTLModel,
        i,j,n for Element of NAT,
        f,f1,f2,g for FinSequence of LTLB_WFF;

theorem
  F |-0 A => B implies F \/ {A} |-0 B
 proof
  A in {A} by TARSKI:def 1;
  then A in F\/{A} by XBOOLE_0:def 3;then
A1: F\/{A} |-0 A by th10;
  assume F |-0 A =>B;
  then F\/{A} |-0 A =>B by mon,XBOOLE_1:7;
  hence F\/{A} |-0 B by A1,th11a;
 end;
