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;
