reserve A for QC-alphabet;
reserve p, q, r, s, p1, q1 for Element of CQC-WFF(A),
  X, Y, Z, X1, X2 for Subset of CQC-WFF(A),
  h for QC-formula of A,
  x, y for bound_QC-variable of A,
  n for Element of NAT;

theorem Th25:
  X1 |-| X2 implies X1 \/ Y |-| X2 \/ Y
proof
  assume X1 |-| X2;
  then Cn(X1) = Cn(X2) by Th20;
  then Cn(X1 \/ Y) = Cn(Cn(X2) \/ Cn(Y)) by Th22
    .= Cn(X2 \/ Y) by Th22;
  hence thesis by Th20;
end;
