theorem Th125:
       L is subst-correct vf-qc-correct implies
  \for(x,A\andB)\imp(\for(x,A)\and\for(x,B)) in G
  proof assume
A1: L is subst-correct vf-qc-correct;
    A\andB\impA in G by Def38;
    then
A2: \for(x,A\andB)\imp\for(x,A) in G by A1,Th115;
    A\andB\impB in G by Def38;
    then
A3: \for(x,A\andB)\imp\for(x,B) in G by A1,Th115;
    \for(x,A\andB)\imp\for(x,A)\imp(\for(x,A\andB)\imp\for(x,B)\imp
    (\for(x,A\andB)\imp\for(x,A)\and\for(x,B))) in G by Th49;
    then (\for(x,A\andB)\imp\for(x,B)\imp
    (\for(x,A\andB)\imp\for(x,A)\and\for(x,B))) in G by A2,Def38;
    hence thesis by A3,Def38;
  end;
