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
  p=h.x & q=h.y & not y in still_not-bound_in h implies All(x,All(y,q))
  => All(x,p) is valid
proof
  assume p=h.x & q=h.y & not y in still_not-bound_in h;
  then All(x,All(y,q) => p) is valid by Th23,Th25;
  hence thesis by Th31;
end;
