reserve A for QC-alphabet;
reserve sq for FinSequence,
  x,y,z for bound_QC-variable of A,
  p,q,p1,p2,q1 for Element of QC-WFF(A);
reserve s,t for bound_QC-variable of A;

theorem
  for x1,x2,y1,y2,z1,z2 being bound_QC-variable of A st Ex(x1,y1,z1,p1) = Ex(
  x2,y2,z2,p2) holds x1 = x2 & y1 = y2 & z1 = z2 & p1 = p2
proof
  let x1,x2,y1,y2,z1,z2 be bound_QC-variable of A such that
A1: Ex(x1,y1,z1,p1) = Ex(x2,y2,z2,p2);
  thus x1 = x2 by A1,Th13;
  Ex(y1,z1,p1) = Ex(y2,z2,p2) by A1,Th13;
  hence thesis by Th17;
end;
