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
  p1 is_an_universal_closure_of p & q1 is_an_universal_closure_of q
  implies (p |-| q iff 'not' p1 |-| 'not' q1)
by Th48;
