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 Th85:
  not x in still_not-bound_in p implies (p => Ex(x,q)) <=> Ex(x,p
  => q) is valid
proof
  assume not x in still_not-bound_in p;
  then
A1: Ex(x,p => q) => (p => Ex(x,q)) is valid by Th83;
  (p => Ex(x,q)) => Ex(x,p => q) is valid by Th84;
  hence thesis by A1,Lm14;
end;
