let X be set ; :: thesis: for x1, x2, x3, x4, x5 being Element of X st X <> {} holds
{x1,x2,x3,x4,x5} is Subset of X
let x1, x2, x3, x4, x5 be Element of X; :: thesis: ( X <> {} implies {x1,x2,x3,x4,x5} is Subset of X )
assume A1: X <> {} ; :: thesis: {x1,x2,x3,x4,x5} is Subset of X
{x1,x2,x3,x4,x5} c= X

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in {x1,x2,x3,x4,x5} or x in X )
assume A2: x in {x1,x2,x3,x4,x5} ; :: thesis: x in X
( not x in {x1,x2,x3,x4,x5} or x = x1 or x = x2 or x = x3 or x = x4 or x = x5 ) by ENUMSET1:def 3;
hence x in X by A1, A2, Def2; :: thesis: verum

end;

then {x1,x2,x3,x4,x5} in bool X by ZFMISC_1:def 1;
hence {x1,x2,x3,x4,x5} is Subset of X by Def2; :: thesis: verum