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 x in still_not-bound_in q & not y in
  still_not-bound_in h implies Ex(x,p) => Ex(y,q) is valid
proof
  assume p=h.x & q=h.y & not x in still_not-bound_in q & not y in
  still_not-bound_in h;
  then ( not x in still_not-bound_in Ex(y,q))& p => Ex(y,q) is valid by Th6
,Th22;
  hence thesis by Th19;
end;
