theorem Th133:
  L is subst-correct vf-qc-correct &
  x in X.a & x nin (vf A).a implies \for(x,A\orB)\imp(A\or\for(x,B)) in G
  proof
    assume
A1: L is subst-correct vf-qc-correct;
    assume
A2: x in X.a & x nin (vf A).a;
    set c = a, a = \notA, b = B;
    x nin (vf a).c by A1,A2; then
A3: \for(x,a\impb)\imp(a\imp\for(x,b)) in G by A2,Def39;
    A\orb\imp(a\impb) in G by Th62;
    then \for(x,A\orB)\imp\for(x,a\impB) in G by A1,Th115;
    then
A4: \for(x,A\orB)\imp(a\imp\for(x,b)) in G by A3,Th45;
    \nota\impA in G & \for(x,B)\imp\for(x,B) in G by Th34,Th65;
    then \nota\or\for(x,B)\impA\or\for(x,B) in G &
    a\imp\for(x,B)\imp\nota\or\for(x,B) in G by Th59,Th82;
    then a\imp\for(x,B)\impA\or\for(x,B) in G by Th45;
    hence thesis by A4,Th45;
  end;
