reserve n for Element of NAT,
  p,q,r,s for Element of HP-WFF;

theorem Th16:
  for A,B being non empty set, C,D being set, f being Function of C,A,
      g being Function of D,B holds pr2(A,B)*[:f,g:] = g*pr2(C,D)
proof
  let A,B be non empty set, C,D be set;
  let f be Function of C,A, g be Function of D,B;
  C = {} implies A = {} or [:C,D:] = {};
  then reconsider F = f*pr1(C,D) as Function of [:C,D:], A;
  D = {} implies A = {} or [:C,D:] = {};
  then reconsider G = g*pr2(C,D) as Function of [:C,D:], B;
  thus pr2(A,B)*[:f,g:] = pr2(A,B)*<:F,G:> by FUNCT_3:77
    .= g*pr2(C,D) by FUNCT_3:62;
end;
