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 Th29:
  p |-| q iff {p} |-| {q}
proof
A1: now
    assume
A2: {p} |-| {q};
    then {q} |- {p} by Th18;
    then
A3: q |- p by Th11;
    {p} |- {q} by A2,Th18;
    then p |- q by Th11;
    hence p |-| q by A3;
  end;
  now
    assume
A4: p |-| q;
    then q |- p;
    then
A5: {q} |- {p} by Th11;
    p |- q by A4;
    then {p} |- {q} by Th11;
    hence {p} |-| {q} by A5,Th18;
  end;
  hence thesis by A1;
end;
