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
  not x in still_not-bound_in p & p '&' All(x,q) is valid implies All(x,
  p '&' q ) is valid
proof
  assume that
A1: not x in still_not-bound_in p and
A2: p '&' All(x,q) is valid;
  (p '&' All(x,q)) => All(x,p '&' q) is valid by A1,Th66;
  hence thesis by A2,CQC_THE1:65;
end;
