let X be set ; :: thesis: for x1, x2 being Element of X st X <> {} holds
{x1,x2} is Subset of X
let x1, x2 be Element of X; :: thesis: ( X <> {} implies {x1,x2} is Subset of X )
assume X <> {} ; :: thesis: {x1,x2} is Subset of X
then A1: ( x1 in X & x2 in X ) by Def1;
{x1,x2} c= X by A1, TARSKI:def 2;
then {x1,x2} in bool X by ZFMISC_1:def 1;
hence {x1,x2} is Subset of X by Def1; :: thesis: verum