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 Th43:
  Ex(x,p '&' q) => (Ex(x,p) '&' Ex(x,q)) is valid
proof
  All(x,p '&' q => q) is valid by Lm1,Th23;
  then
A1: Ex(x,p '&' q) => Ex(x,q) is valid by Th35;
  All(x,p '&' q => p) is valid by Lm1,Th23;
  then Ex(x,p '&' q) => Ex(x,p) is valid by Th35;
  hence thesis by A1,Lm3;
end;
