let A, B be finite set ; :: thesis: ( card A < card B implies ex x being set st x in B \ A )
assume card A < card B ; :: thesis: ex x being set st x in B \ A
then not B c= A by NAT_1:44;
then consider x being set such that
00: ( x in B & x nin A ) by TARSKI:def 3;
take x ; :: thesis: x in B \ A
thus x in B \ A by 00, XBOOLE_0:def 5; :: thesis: verum