reserve Al for QC-alphabet;
reserve i,j,k for Nat,
  A,D for non empty set;
reserve f1,f2 for Element of Funcs(Valuations_in(Al,A),BOOLEAN),
  x,x1,y for bound_QC-variable of Al,
  v,v1 for Element of Valuations_in(Al,A);
reserve ll for CQC-variable_list of k,Al;
reserve p,q,s,t for Element of CQC-WFF(Al),
  J for interpretation of Al,A,
  P for QC-pred_symbol of k,Al,
  r for Element of relations_on A;

theorem
  Valid('not' 'not' p,J) = Valid(p,J)
proof
  now
    let v;
    thus Valid('not' 'not' p,J).v = 'not'(Valid('not' p,J).v) by Th10
      .= 'not'('not'(Valid(p,J).v)) by Th10
      .= Valid(p,J).v;
  end;
  hence thesis by FUNCT_2:63;
end;
