theorem
  [:A1,A2:] = { [x1,x2] : x1 in A1 & x2 in A2 }
proof
  thus [:A1,A2:] c= { [x1,x2] : x1 in A1 & x2 in A2 }
  proof
    let a be object;
    assume
A1: a in [:A1,A2:];
    then reconsider x = a as Element of [:X1,X2:];
A2: x = [x`1,x`2];
    x`1 in A1 & x`2 in A2 by A1,MCART_1:10;
    hence thesis by A2;
  end;
  let a be object;
  assume a in { [x1,x2] : x1 in A1 & x2 in A2 };
  then ex x1,x2 st a = [x1,x2] & x1 in A1 & x2 in A2;
  hence thesis by ZFMISC_1:87;
end;
