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
  Ex(x,p '&' q) is valid implies Ex(x,p) '&' Ex(x,q) is valid
proof
  assume
A1: Ex(x,p '&' q) is valid;
  Ex(x,p '&' q) => (Ex(x,p) '&' Ex(x,q)) is valid by Th43;
  hence thesis by A1,CQC_THE1:65;
end;
