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 Th4:
  X |- p & X c= Y implies Y |- p
proof
  assume that
A1: X |- p and
A2: X c= Y;
A3: p in Cn(X) by A1,CQC_THE1:def 8;
  Cn(X) c= Cn(Y) by A2,CQC_THE1:18;
  hence thesis by A3,CQC_THE1:def 8;
end;
