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 Th35:
  X |- All(x,p) iff X |- p
proof
  thus X |- All(x,p) implies X |- p
  proof
A1: X |- All(x,p) => p by CQC_THE1:56;
    assume X |- All(x,p);
    hence thesis by A1,CQC_THE1:55;
  end;
  thus thesis by CQC_THE2:90;
end;
