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 Th15:
  |- X iff {}(CQC-WFF(A)) |- X
proof
  hereby
    assume
A1: |- X;
    now
      let p;
      assume p in X;
      then p is valid by A1;
      hence {}(CQC-WFF(A)) |- p by CQC_THE1:def 9;
    end;
    hence {}(CQC-WFF(A)) |- X;
  end;
  thus thesis by CQC_THE1:def 9;
end;
