theorem     :: ZFMISC_1:24
  {x} c= {y} implies {x} = {y}
proof
  assume
A1: {x} c= {y};
  now
    let i be object;
    assume
A2: i in I;
    then {x}.i c= {y}.i by A1;
    then {x.i} c= {y}.i by A2,Def1;
    then
A3: {x.i} c= {y.i} by A2,Def1;
    thus {x}.i = {x.i} by A2,Def1
      .= {y.i} by A3,ZFMISC_1:18
      .= {y}.i by A2,Def1;
  end;
  hence thesis;
end;
