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 Th3:
  X |- p & {p} |- q implies X |- q
proof
  assume that
A1: X |- p and
A2: {p} |- q;
  p in Cn(X) by A1,CQC_THE1:def 8;
  then {p} c= Cn(X) by ZFMISC_1:31;
  then
A3: Cn({p}) c= Cn(X) by CQC_THE1:15,16;
  q in Cn({p}) by A2,CQC_THE1:def 8;
  hence thesis by A3,CQC_THE1:def 8;
end;
