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 Th27:
  X1 |-| X2 & Y |- X1 implies Y |- X2
proof
  assume that
A1: X1 |-| X2 and
A2: Y |- X1;
  X1 |- X2 by A1,Th18;
  hence thesis by A2,Th9;
end;
