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 Th37:
  All(x,p '&' q) <=> (All(x,p) '&' All(x,q)) is valid
proof
  All(x,p '&' q) => (All(x,p) '&' All(x,q)) is valid & (All(x,p) '&' All(x
  ,q)) => All(x,p '&' q) is valid by Th36;
  hence thesis by Lm14;
end;
