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 Th66:
  not x in still_not-bound_in p implies (p '&' All(x,q)) => All(x,
  p '&' q) is valid
proof
  assume
A1: not x in still_not-bound_in p;
  All(x,q) => q is valid by CQC_THE1:66;
  then
A2: p '&' All(x,q) => p '&' q is valid by Lm9;
  not x in still_not-bound_in All(x,q) by Th5;
  then not x in still_not-bound_in p '&' All(x,q) by A1,Th8;
  hence thesis by A2,CQC_THE1:67;
end;
