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
  p |-| q & X |- p implies X |- q
proof
  assume that
A1: p |-| q and
A2: X |- p;
A3: X |- {p} by A2,Th10;
  {p} |-| {q} by A1,Th29;
  then X |- {q} by A3,Th27;
  hence thesis by Th10;
end;
