reserve A for QC-alphabet;
reserve sq for FinSequence,
  x,y,z for bound_QC-variable of A,
  p,q,p1,p2,q1 for Element of QC-WFF(A);
reserve s,t for bound_QC-variable of A;
reserve F,G,H,H1 for Element of QC-WFF(A);
reserve x,y,z for bound_QC-variable of A,
  k,n,m for Nat,
  P for ( QC-pred_symbol of k, A),
  V for QC-variable_list of k, A;

theorem Th50:
  H is universal implies (F is_immediate_constituent_of H iff F =
  the_scope_of H)
proof
  assume H is universal;
  then H = All(bound_in H, the_scope_of H) by Th6;
  hence thesis by Th46;
end;
