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 Th41:
  Ex(x,p 'or' q) <=> (Ex(x,p) 'or' Ex(x,q)) is valid
proof
  Ex(x,p 'or' q) => (Ex(x,p) 'or' Ex(x,q)) is valid & (Ex(x,p) 'or' Ex(x,q
  )) => Ex(x,p 'or' q) is valid by Th40;
  hence thesis by Lm14;
end;
