theorem     :: ZFMISC_1:8
  {x} = {A,B} implies x = A & x = B
proof
  assume
A1: {x} = {A,B};
  now
    let i be object;
    assume
A2: i in I;
    then {x.i} = {x}.i by Def1
      .= {A.i,B.i} by A1,A2,Def2;
    hence x.i = A.i by ZFMISC_1:4;
  end;
  hence x = A;
  now
    let i be object;
    assume
A3: i in I;
    then {x.i} = {x}.i by Def1
      .= {A.i,B.i} by A1,A3,Def2;
    hence x.i = B.i by ZFMISC_1:4;
  end;
  hence thesis;
end;
