reserve X,Y for set, x,y,z for object, i,j,n for natural number;
reserve
  n for non empty Nat,
  S for non empty non void n PC-correct PCLangSignature,
  L for language MSAlgebra over S,
  F for PC-theory of L,
  A,B,C,D for Formula of L;
reserve
  J for non empty non void Signature,
  T for non-empty MSAlgebra over J,
  X for non empty-yielding GeneratorSet of T,
  S1 for J-extension non empty non void n PC-correct QC-correct
  QCLangSignature over Union X,
  L for non-empty Language of X extended_by ({},the carrier of S1), S1,
  G for QC-theory of L,
  A,B,C,D for Formula of L;
reserve x,y,z for Element of Union X;
reserve x0,y0,z0 for Element of Union (X extended_by ({},the carrier of S1));

theorem Th108:
  for a being SortSymbol of J
  st x in X.a & x nin (vf A).a & \for(x,A\impB) in G
  holds A\imp\for(x,B) in G
  proof let a be SortSymbol of J;
    assume
A1: x in X.a & x nin (vf A).a & \for(x,A\impB) in G; then
    \for(x,A\impB)\imp(A\imp\for(x,B)) in G by Def39;
    hence thesis by Def38,A1;
  end;
