theorem Th46:
  B c= C implies B ^ D c= C ^ D
proof
  deffunc F(Element of DISJOINT_PAIRS A, Element of DISJOINT_PAIRS A) = $1 \/
  $2;
  defpred P[set,set] means $1 in B & $2 in D;
  defpred Q[set,set] means $1 in C & $2 in D;
  set X1 = { F(s,t): P[s,t] };
  set X2 = { F(s,t): Q[s,t] };
  assume B c= C;
  then
A1: P[s, t] implies Q[s, t];
  X1 c= X2 from FRAENKEL:sch 2(A1);
  hence thesis by XBOOLE_1:26;
end;
