theorem
  F|-('G' p)=>q implies F\/{p}|-q
 proof
  p in {p} by TARSKI:def 1;
  then p in F\/{p} by XBOOLE_0:def 3;
  then F\/{p}|-p by Th42;
  then A1: F\/{p}|-'G' p by Th54;
  assume F|-('G' p)=>q;
  then F\/{p}|-('G' p)=>q by Th56;
  hence F\/{p}|-q by A1,Th43;
 end;
