reserve A for QC-alphabet;
reserve X,T for Subset of CQC-WFF(A);
reserve F,G,H,p,q,r,t for Element of CQC-WFF(A);
reserve s,h for QC-formula of A;
reserve x,y for bound_QC-variable of A;
reserve f for FinSequence of [:CQC-WFF(A),Proof_Step_Kinds:];
reserve i,j for Element of NAT;

theorem
  All(x,All(y,p)) => All(y,All(x,p)) is valid & All(x,y,p) => All(y,x,p)
  is valid
proof
  not y in still_not-bound_in All(y,p) by Th5;
  then
A1: not y in still_not-bound_in All(x,All(y,p)) by Th5;
  All(x,All(y,p) => p) is valid & All(x,All(y,p) => p) => (All(x,All(y,p))
  => All(x,p)) is valid by Th23,Th30,CQC_THE1:66;
  then All(x,All(y,p)) => All(x,p) is valid by CQC_THE1:65;
  hence All(x,All(y,p)) => All(y,All(x,p)) is valid by A1,CQC_THE1:67;
  then All(x,y,p) => All(y,All(x,p)) is valid by QC_LANG2:14;
  hence thesis by QC_LANG2:14;
end;
