reserve i for object, I for set,
  f for Function,
  x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;

theorem     :: ZFMISC_1:18
  {x} (/\) {y} = {x} implies x = y
proof
  assume
A1: {x} (/\) {y} = {x};
    now
      let i be object;
      assume
A2:   i in I;
      then {x.i} /\ {y.i} = {x.i} /\ {y}.i by Def1
        .= {x}.i /\ {y}.i by A2,Def1
        .= ({x} (/\) {y}).i by A2,PBOOLE:def 5
        .= {x.i} by A1,A2,Def1;
      hence x.i = y.i by ZFMISC_1:12;
    end;
    hence thesis;
end;
