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 Th64:
  All(x,p '&' q) => (p '&' All(x,q)) is valid
proof
A1: All(x,p '&' q) => (p '&' q) is valid by CQC_THE1:66;
A2: not x in still_not-bound_in All(x,p '&' q) by Th5;
  (p '&' q) => q is valid by Lm1;
  then All(x,p '&' q) => q is valid by A1,LUKASI_1:42;
  then
A3: All(x,p '&' q) => All(x,q) is valid by A2,CQC_THE1:67;
  (p '&' q) => p is valid by Lm1;
  then All(x,p '&' q) => p is valid by A1,LUKASI_1:42;
  hence thesis by A3,Lm3;
end;
