reserve Al for QC-alphabet;
reserve i,j,k for Nat,
  A,D for non empty set;
reserve f1,f2 for Element of Funcs(Valuations_in(Al,A),BOOLEAN),
  x,x1,y for bound_QC-variable of Al,
  v,v1 for Element of Valuations_in(Al,A);
reserve ll for CQC-variable_list of k,Al;
reserve p,q,s,t for Element of CQC-WFF(Al),
  J for interpretation of Al,A,
  P for QC-pred_symbol of k,Al,
  r for Element of relations_on A;
reserve u,w,z for Element of BOOLEAN;
reserve w,v2 for Element of Valuations_in(Al,A),
  z for bound_QC-variable of Al;

theorem
  for A be non empty set, Y, Z be bound_QC-variable of Al,
   V1, V2 be Element of Valuations_in(Al,A)
  ex v being Element of Valuations_in(Al,A) st
   (for x being bound_QC-variable of Al st x <> Y holds v.x = V1.x) &
   v.Y = V2.Z by Lm3;
