let X be set ; :: thesis: X /\ {} = {}
thus X /\ {} c= {} :: according to XBOOLE_0:def 10 :: thesis: {} c= X /\ {}

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in X /\ {} or x in {} )
assume x in X /\ {} ; :: thesis: x in {}
hence x in {} by XBOOLE_0:def 4; :: thesis: verum

end;

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in {} or x in X /\ {} )
assume x in {} ; :: thesis: x in X /\ {}
hence x in X /\ {} by XBOOLE_0:def 1; :: thesis: verum