reserve A for QC-alphabet;
reserve i,j,k for Nat;
reserve f for Substitution of A;
reserve x,y for bound_QC-variable of A;
reserve a for free_QC-variable of A;
reserve p,q for Element of QC-WFF(A);
reserve l,l1,l2,ll for FinSequence of QC-variables(A);
reserve r,s for Element of CQC-WFF(A);

theorem Th21:
  (p '&' q).x = (p.x) '&' (q.x)
proof
  set pq = p '&' q;
A1: p '&' q is conjunctive by QC_LANG1:def 20;
  then the_left_argument_of pq = p & the_right_argument_of pq = q by
QC_LANG1:def 25,def 26;
  hence thesis by A1,Th20;
end;
