reserve Al for QC-alphabet;
reserve b,c,d for set,
  X,Y for Subset of CQC-WFF(Al),
  i,j,k,m,n for Nat,
  p,p1,q,r,s,s1 for Element of CQC-WFF(Al),
  x,x1,x2,y,y1 for bound_QC-variable of Al,
  A for non empty set,
  J for interpretation of Al, A,
  v for Element of Valuations_in(Al,A),
  f1,f2 for FinSequence of CQC-WFF(Al),
  CX,CY,CZ for Consistent Subset of CQC-WFF(Al),
  JH for Henkin_interpretation of CX,
  a for Element of A,
  t,u for QC-symbol of Al;
reserve L for PATH of q,p,
  F1,F3 for QC-formula of Al,
  a for set;
reserve C,D for Element of [:CQC-WFF(Al),bool bound_QC-variables(Al):];
reserve K,L for Subset of bound_QC-variables(Al);

theorem Th26:
  still_not-bound_in {p} = still_not-bound_in p
proof
A1: now
    let a be object;
    assume a in still_not-bound_in {p};
    then consider b such that
A2: a in b & b in {still_not-bound_in q : q in {p}} by TARSKI:def 4;
    ex q st ( b = still_not-bound_in q)&( q in {p}) by A2;
    hence a in still_not-bound_in p by A2,TARSKI:def 1;
  end;
  now
    let a be object such that
A3: a in still_not-bound_in p;
    set b = still_not-bound_in p;
    p in {p} by TARSKI:def 1;
    then b in {still_not-bound_in q : q in {p}};
    hence a in still_not-bound_in {p} by A3,TARSKI:def 4;
  end;
  hence thesis by A1,TARSKI:2;
end;
