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
  All(x,p '&' q) is valid iff All(x,p) '&' All(x,q) is valid
proof
  All(x,p '&' q) <=> (All(x,p) '&' All(x,q)) is valid by Th37;
  hence thesis by Lm15;
end;
