theorem Th117:
       L is subst-correct vf-qc-correct implies
  \for(x,A\impB)\imp(\for(x,\notB)\imp\for(x,\notA)) in G
  proof assume
A1: L is subst-correct vf-qc-correct;
    (A\impB)\imp(\notB\imp\notA) in G by Th57;
    then
A2: \for(x,A\impB)\imp(\for(x,\notB\imp\notA)) in G by A1,Th115;
    \for(x,\notB\imp\notA)\imp(\for(x,\notB)\imp\for(x,\notA)) in G
    by A1,Th109;
    hence \for(x,A\impB)\imp(\for(x,\notB)\imp\for(x,\notA)) in G by A2,Th45;
  end;
